FROM QUANTA TO QUARKS

 

“1. Problems with the Rutherford model of the atom led to a search for a model that would better explain the observed phenomena.  ” (syllabus)

 

“Students learn to discuss the structure of the Rutherford model of the atom, the existence of the nucleus and electron orbits” (syllabus)

 

Under Rutherford’s direction, Hans Geiger and Earnest Marsden fired alpha particles at thin gold foil in an evacuated container and detected their path.      Most of the alpha particles went through the gold foil undeflected, a few were deflected by small amounts and a very few were deflected by angles greater than 90o, i.e. they bounced back.                                                                                

Most going through undeflected indicated that most of the atom was empty space. The alpha particles that bounced back indicated that they were deflected by something massive and positively charged. Rutherford interpreted this to propose the planetary model of the atom i.e. a small positive nucleus with electrons orbiting the nucleus and electrostatic attraction supplying the centripetal force.

 

“Students learn to analyse the significance of the hydrogen spectrum in the development of Bohr’s model of the atom” (syllabus)

 

  1. Electrons orbiting the nucleus are oscillating electric charges and should be continuously emitting electromagnetic radiation. This does not occur.

With the emission of electromagnetic radiation the electrons should gradually lose energy and spiralinto the nucleus. However atoms are stable.

A spiralling electron should emit radiation of all frequencies, producing a continuous spectrum. This is in contrast to the line spectrum of elements that is observed.

  1. Bohr proposed that electrons could orbit only in certain orbits or energy levels. Under normal conditions it will follow the innermost orbit, which has the least energy and is known as the ground state.

While it is folowing an allowed orbit the electron will not emit radiation or lose energy.

An electron can absorb energy and jump up to a higher energy level. In this energy level it is unstable and will return to its former energy level in one or more steps. As it drops back to a lower energy level it will give out a photon of electromagnetic radiation. The difference between the two energy levels will determine the frequency and hence the colour of the radiation which is governed by Planck’s equation; E = hf.

 

 

 

“Students learn to define Bohr’s postulates” (syllabus)

 

Bohr proposed that electrons could orbit only in certain orbits or energy levels. Under normal conditions it will follow the innermost orbit, which has the least energy and is known as the ground state.

While it is following an allowed orbit the electron will not emit radiation or lose energy.

An electron can absorb energy and jump up to a higher energy level. In this energy level it is unstable and will return to its former energy level in one or more steps. As it drops back to a lower energy level it will give out a photon of electromagnetic radiation. The difference between the two energy levels will determine the frequency and hence the colour of the radiation which is governed by Planck’s equation; E = hf.

 

 

“Students learn to discuss Planck’s contribution to the concept of quantised energy” (syllabus)

 

Planck’s contribution to the concept of quantised energy came from his study of black bodies. A black body is one that will absorb all radiation that hits it. At equilibrium the amount of incident radiation equals the amount of emitted radiation so the temperature remains constant.

Planck investigated the spectra emitted by cavity radiators and observed that the peak wavelength was dependent on the temperature of the object and not on the material that the cavity radiator was made of.

   Cavity Radiator

 

Planck proposed that the atoms inside the cavity oscillated back and forth, emitting radiation, similar to the way a radio antenna works. Energy would be absorbed by the walls of the cavity radiator and re-emitted. Oscillating atoms inside the cavity could receive electromagnetic radiation, but only at certain wavelengths. He proposed that atoms could only receive and emit energy in fixed amounts consistent with the equation E = hf = hc/l, i.e. energy was quantised.

 

 

Emitted radiation comes in whole number multiples of a specific quantity; no fraction values are allowed.

 

 

 

 

“Students learn to describe how Bohr’s postulates led to the development of a mathematical model to account for the existence of the hydrogen spectrum:

1/l = R(1/nf2 – 1/ni2 ) ” (syllabus)

 

The wavelengths of the four visible lines of the hydrogen spectrum were first determined by Anders Angstrom in the mid nineteenth century. Johann Balmer found an equation that would fit these wavelengths and his equation was later modified by Janne Rydberg to 1/l = R(1/22 – 1/n2 ) where n is an integer (3,4,5 or 6) and R is a constant (Rydberg’s constant = 1.097 x 107 m-1). Both Balmer and Rydberg used empirical methods to develop the equation i.e. they found an equation that would fit the numbers with no explanation as to why it worked.

            Niels Bohr proposed that electrons could only orbit in certain stable orbits of fixed energy levels. He began by equating the angular momentum of the electron to multiples of h/2p and proceded to develop a mathematical model for the allowed electron orbits and ended up with the Rydberg equation, 1/l = R(1/nf2 – 1/ni2 ). Bohr’s analysis predicted spectral lines outside the visible region and these were later discovered by Lyman, Paschen, Brackett and Pfund.

 

A site that shows how the Bohr model can be used to derive the Rydberg equation is

http://www.launc.tased.edu.au/online/sciences/Physics/brhydrogen.html

 

“Students learn to discuss the limitations of the Bohr model of the hydrogen atom” (syllabus)

 

The Bohr model does not allow the theoretical calculation of spectral lines other than hydrogen.

It has trouble explaining what happens to atoms with more than one valence electron.

It does not explain why spectral lines are not of equal intensity.

It does not explain the Zeeman effect or hyperfine splitting.

 

 

 

“Students perform a first-hand investigation to observe the visible components of the hydrogen spectrum” (syllabus)

 

To complete this section of the syllabus properly your teacher should set up a hydrogen discharge tube and you should observe it through a spectroscope. The following illustration of the hydrogen spectrum is taken from

 

http://www.physchem.co.za/Atomic/Hydrogen%20Spectrum.htm

 

Balmer series lines

 

 

           

 

 Some other websites that show the hydrogen spectrum are listed below.

http://230nsc1.phy-astr.gsu.edu/hbase/hyde.html

http://cat.middlebury.edu/~chem/chemistry/class/general/ch103/hatom/index.html

http://csep10.phys.utk.edu/astr162/lect/light/absorption.html

 

“Students process and present diagrammatic information to illustrate Bohr’s explanation of the Balmer series” (syllabus)

 

The Balmer series represents the situation where electrons drop down to the second energy level i.e. where nf = 2. It was widely studied because its spectral lines are in the visible region of the spectrum. It is represented in the diagram below.

 

                       

                                                            Balmer Series

 

Similar diagrams can be drawn for the Lyman series (nf = 1, the ground state), the Paschen series (nf = 3), the Brackett series (nf = 4), and the Pfund series (nf = 5).

                                                Series for Electron Energy Levels

 

 

 

 

The energy levels can also be represented in a diagram like the one below. In each case the amount of energy stated is the energy released when ni = T. This is the energy required to completely release an electron and is known as the ionisation energy.

For example, the energy required to completely remove a hydrogen electron in its ground state can be found by:

(i) Calculating the wavelength of the photon required

1/l = R(1/nf2 – 1/ni2 )

1/l = 1.097 x 107 (1/12 – 1/T2)

1/l = 1.097 x 107 (1– 0) = 1.097 x 107

l = 9.1158 x 10-8m (Note that this is in the U.V. region)

 

(ii) Calculating the energy of the photon in joules.

E = hf = hc/l

E = 6.626 x 10-34 x 3 x 108/ 9.1158 x 10-8 = 2.181 x 10-18 Joules

 

(iii) Convert to electron volts.

An electron Volt is the energy required to accelerate an electron through a potential difference of 1 volt. W = qV             = 1.6 x 10-19 x 1           1 eV = 1.6 x 10-19 J

2.181 x 10-18 Joules = 2.181 x 10-18 / 1.6 x 10-19 eV = 13.6 eV

           

            Electron Energy Levels for Hydrogen

 

“Students solve problems and analyse information using: 1/l = R(1/nf2 – 1/ni2 ) ” (syllabus)

 

  1. The Balmer series of spectral lines occurs when nf = 2. It includes the visible lines of the hydrogen spectrum. It is not the ground state. Calculate the wavelengths of the four visible lines of the hydrogen spectrum.

 

A.  1/l = R {(1/nf)2 – (1/ni)2}       

1/l = 1.097 x 107{(1/2)2 – (1/3)2}       l = 6.563 x 10-7 m.     

1/l = 1.097 x 107{(1/2)2 – (1/4)2}       l = 4.862 x 10-7 m.     

1/l = 1.097 x 107{(1/2)2 – (1/5)2}       l = 4.341 x 10-7 m.

1/l = 1.097 x 107{(1/2)2 – (1/6)2}       l = 4.102 x 10-7 m.

 

“Students analyse secondary information to identify the difficulties with the Rutherford-Bohr model, including its inability to completely explain:

-          the spectra of larger atoms

-          the relative intensity of spectral lines

-          the existence of hyperfine spectral lines

-          the Zeeman effect” (syllabus)

 

 

Larger atoms:

While the mathematical model developed by Bohr works well in predicting hydrogen spectral lines it has not been successful with larger atoms. It has had limited success with helium and group I metals but has been unable to predict spectral lines of other atoms. Bohr made no provision for restricting the number of electrons in each orbit. The maximum number of electrons in each orbit is 2n2 and no two electrons can have exactly the same energy levels (Pauli exclusion principle). Bohr’s mathematical model did not allow for these restrictions and consequently does not fit larger atoms.

 

Intensity:

Electrons drop from a high energy level to a lower energy level and emit a photon of light as they do so. The number of electrons dropping between different energy levels varies and so too does the intensity of the different wavelengths.

 

Hyperfine spectral lines:

Hyperfine splitting of spectral lines results from energy level changes in atoms of different isotopes and also from the interaction of nuclear spin with electron spin.

 

Zeeman effect:

The Zeeman effect refers to the splitting of spectral lines when they are placed in a strong magnetic field. It occurs due the interaction of the electron spin and the magnetic field.

 

 

 

“2. The limitations of classical physics gave birth to quantum physics.” (syllabus)

 

“Students learn to describe the impact of de Broglie’s proposal that any kind of particle has both wave and particle properties” (syllabus)

 

The implications of De Broglie’s wave-particle duality theory allow the use of the wave nature of things considered as particles. It explained the stability of electron orbits in atoms by proposing that the orbit of these particles was made up of a whole number of wavelengths. He said that the electron could rise to a higher energy level by increasing its circumference by multiples of its wavelength. Electrons (and all particles) have both wave and particle properties.Electron diffraction allowed the structure of crystals to be determined with greater accuracy while the electron microscope allows such things as cell components to be studied in much greater detail than is possible with the light microscope.

 

 

 

“Students learn to define diffraction and identify that interference occurs between waves that have been diffracted” (syllabus)

 

            Diffraction is the spreading out or bending of waves as they pass around a barrier or through an aperture. It occurs when water waves go past a rock or post and join up again on the other side. It also occurs with other types of waves including electromagnetic waves.

 

            In 1665 Francesco Grimaldi showed that when sunlight passed through a very small hole, it spread out and showed coloured fringes at the edge if it was projected onto a screen. He had demonstrated the diffraction of light.

 

            Diffraction was further demonstrated in 1704 by Newton when he placed a slightly curved convex lens on a sheet of flat glass. This produced concentric circles of bright and dark bands as the diffracted light produced interference patterns. This phenomenon is known as “Newton’s rings”.

 

            In 1803 Thomas Young further demonstrated the diffraction of light with his double slit experiment. He shone light first through a single slit and then through two slits and observed interference patterns on a screen. The single slit ensured coherent sources at the two slits since they had both come from the same wave rather than from two separate waves.

 

            These diffraction and interference effects demonstrated the wave nature of light. This was extended to other electromagnetic waves in 1912 when Max von Laue demonstrated the diffraction of x-rays as they passed through crystal lattices and in 1913 when William Henry Bragg and William Laurence Bragg used x-ray diffraction to determine the crystal structure of diamond and several minerals.

 

            In 1924 Louis de Broglie proposed that waves and matter were inter-related and that matter could be represented as waves where l = h / mv. This phenomenon is known as the wave-particle duality where waves have some matter properties and matter has some wave properties. This was demonstrated by Americans Davisson and Germer in 1927 and by the Englishman George Thomson in 1928 when they demonstrated the diffraction of electrons by bouncing a beam of cathode rays off a crystal of nickel.

 

            While x-rays have the advantage of having wavelengths that approximate the separation of atoms in crystals and hence show maximum diffraction, electrons have the advantage of having a charge and so can be focused. This has enabled the development of the electron microscope.

 

            It is interesting that Joseph John Thomson received the Nobel Prize in 1906 for his work in showing that electrons were particles and his son George Thomson received the Nobel Prize in 1937 (jointly with Clinton Davisson) for his work in showing that electrons are waves.

 

“Students learn to describe the confirmation of de Broglie’s proposal by Davisson and Germer” (syllabus)

 

Davisson and Germer demonstrated electron diffraction patterns and thus showed that electrons have a wave nature. They reflected electrons off the surface of a nickel crystal and found that certain angles produced diffraction patterns. While Davisson and Germer were demonstrating electron diffraction in America, George Thomson (son of J.J.) independently demonstrated electron diffraction in England. Davisson and Thomson shared the Nobel Prize for their work in 1937.

 

 

“Students learn to explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis” (syllabus)

 

De Broglie proposed that the circumference of the electron’s orbit was a whole number of wavelengths. He said that the electron could rise to a higher energy level by increasing its circumference by multiples of its wavelength.

 

 

 

“Students solve problems using: l = h/mv” (syllabus)

 

What is the wavelength of      (i) an electron travelling at 106 ms-1?

(ii) a 65 kg physics teacher running at 5 ms-1?

 

(i) l = h / mv = 6.63 x 10-34 / 9.1 x 10-31 x 106            = 7.3 x 10-10 m.

(ii) l = h / mv = 6.63 x 10-34 / 65 x 5 = 2.0 x 10-36 m.

 

 

 

“Students gather, process, analyse and present information and use available evidence to assess the contributions made by Heisenberg and Pauli to the development of atomic theory” (syllabus)

 

  1. Heisenberg’s uncertainty principle states that it is impossible to measure both the momentum and the position of a particle at the same time. The observation of one property disturbs the system such that the other changes.
  2. Pauli’s exclusion principle states that no two electrons in an atom can have the same set of quantum numbers.
  3. Pauli predicted the neutrino on the basis of energy loss in beta decay.

 

 

 

 

“3. The work of Chadwick and Fermi in producing artificial transmutations led to practical applications of nuclear physics.” (syllabus)

 

“Students learn to define components of the nucleus (protons and neutrons) as nucleons and contrast their properties. ” (syllabus)

 

 The major nuclear particles, i.e. protons and neutrons, are known as nucleons.

Protons and neutrons have similar mass with the neutron being slightly heavier. (Proton = 1.673 x 10-7 kg, Neutron = 1.675 x 10-7 kg)

The proton has an electrical charge equal in magnitude and opposite in sign to that of the electron. (Charge on proton = + 1.602 x 10-19 Coulomb).

The neutron has no electric charge.

Both protons and neutrons are composed of three quarks.

Particles composed of quarks are known as “hadrons” and those composed of three quarks are known as “baryons”. So protons and neutrons are both hadrons and baryons (as opposed to mesons which are composed of two quarks – these are hadrons but not baryons).

Protons and neutrons are composed of up quarks which have an electric charge of  +2/3 e- and of down quarks that have a charge of – 1/3 e-.

Protons consist of two up quarks and a down quark while neutrons consist of two down quarks and an up quark.

 

“Students learn to discuss the importance of conservation laws to Chadwick’s discovery of the neutron. ” (syllabus)

 

Chadwick’s discovery of the neutron was based on his interpretation of the work of Bothe and Becker and the subsequent work of Frederic and Irene Joliot.

 

Bothe and Becker bombarded beryllium with alpha rays and noticed that it gave off a penetrating radiation that was undeflected by electric and magnetic fields. They incorrectly thought that these rays were high-energy gamma rays.

 

Frederic and Irene Joliot repeated Bothe and Becker’s experiment and placed a paraffin sheet in front of the penetrating radiation. They found that protons were emitted from the paraffin. They calculated the energy required by gamma rays to knock out a proton and found it to be unacceptably high. It seemed that either the laws of conservation did not hold or that the radiation was not gamma rays.

 

James Chadwick read the Joliots’ research and repeated their experiment as well as bombarding several light elements such as helium, lithium and nitrogen with the penetrating radiation and measuring the recoil of their nuclei. Chadwick examined the energy of the penetrating radiation and the energy of the emitted protons and found that if it was gamma radiation then the energy would be insufficient to knock protons out of the paraffin. He also studied the energy of recoil of the several light elements that he bombarded with the penetrating radiation. He was faced with the dilema of either rejecting conservation laws or coming up with an alternative explanation. He found that the conservation laws of energy and momentum would hold if the radiation consisted of neutral particles of about the same mass as the proton.

 

 

 

“Students learn to define the term “transmutation”. ” (syllabus)

 

Transmutation is the changing of one element into another. It can occur naturally by the element emitting an alpha particle or a beta particle, or artificially by bombarding the nucleus with another particle.

 

 

“Students learn to describe nuclear transmutations due to natural radioactivity” (syllabus)

 

Radioactivity was first discovered by Henri Becquerel in 1896. Further investigation by Earnest Rutherford showed that there were two types of radiation given off; alpha rays and beta rays. ( Paul Villard later found a third type of radiation which he called gamma rays)

The emission of an alpha particle (2 protons + 2 neutrons) or a beta particle (electron) changes the atom to a different substance i.e. the atom undergoes nuclear transmutation.

e.g.                     à      + alpha particle

 

  à    + beta particle

 

Rutherford found that transmutation could occur when substances are bombarded with alpha particles. He bombarded nitrogen with alpha particles and found that protons were given off. He reasoned that this could have occurred in one of two ways.

 

 +     à    +  +

 

                        or

                         +     à    + 

 In 1925 Blackett used a cloud chamber to show that only two particles were produced. This showed that the reaction represented by the second equation took place and nitrogen underwent transmutation into oxygen.

 

“Students learn to describe Fermi’s initial experimental observation of nuclear fission. ” (syllabus)

 

Following the discovery by Curie and Joliot of artificial radioactivity (1934), he demonstrated that nuclear transformation occurs in almost every element subjected to neutron bombardment. This work resulted in the discovery of slow neutrons that same year, leading to the discovery of nuclear fission and the production of elements lying beyond what was until then the Periodic Table. Copied from http://www.nobel.se/physics/laureates/1938/fermi-bio.html

 

. In 1934, while at the University of Rome, Fermi began experiments where he bombarded a variety of elements with neutrons. He discovered that slow moving neutrons were especially effective in producing radioactive atoms. Not realizing he had split the atom, Fermi announced what he thought were elements beyond uranium. Fermi won the 1938 Nobel Prize for physics for his work on nuclear processes. Also in 1938 two German physicists, Lise Meitner and Otto Frisch performed a similar experiment where they split a uranium atom. They named the process of splitting atoms "nuclear fission." Copied from http://www.lucidcafe.com/library/95sep/fermi.html

 

 

“Students learn to discuss Pauli’s suggestion of the existence of neutrino and relate it to the need to account for the energy distribution of electrons emitted in b-decay. ” (syllabus)

 

Beta decay seemed to result in some energy loss. While some scientists, such as Bohr, suggested that conservation laws might not hold for sub-atomic particles, Pauli suggested that the energy was carried away by another sub-atomic particle. He predicted that the particle had no charge, had high penetrating power and very little mass.

 

Enrico Fermi constructed a theory of beta decay based on Pauli’s predictions and studied the shape of the spectrum produced by beta decay. He concluded that the mass of the particle was very close to zero. He named the particle the”neutrino” (little neutral one in Italian).

 

 

 

“Students learn to evaluate the relative contributions of electrostatic and gravitational forces between nucleons. ” (syllabus)

 

The relative contributions of the electrostatic and gravitational forces between nucleons is best understood by doing a numerical example.

1.      The separation of nucleons is in the order of 10-15m. Calculate the force of repulsion between two protons at this distance.

 

F = kq1q2 / r2         = 9.0 x 109 (1.6 x 10-19)2 / (1.0 x 10-15)2           = 230N

 

2.      What is the gravitational attraction between two protons that are 10-15 m apart?

 

      F = Gm1m2/ r2 = 6.67 x 10-11 (1.673 x 10-27)2 /(1.0 x 10-15)2          = 1.87 x 10-34N

 

3.      What is the ratio of the electrostatic force to the gravitational force of two protons that are 10-15 m apart?

 

230 / 1.87 x 10-34 = 1.2 x 1036 : 1

Note that the electrostatic force is huge compared with the gravitational force.

 

“Students learn to account for the need for the strong nuclear force and describe its properties.” (syllabus)

 

Two protons in a nucleus are separated by around 10-15 metres and have an electrostatic force of repulsion of around 230 N between. Since nuclei are stable there has to be a stronger force than this to hold the nucleus together. This is the strong nuclear force and acts only over very small distances. It is a force between nucleons and acts between protons and protons, neutrons and neutrons as well as protons and neutrons. At very close distances nucleons repel each other but the repulsive force turns to one of attraction at separations of just under 10-15 m. At separations of about 3 x 10-15 m the strong nuclear force drops to zero.

 

                       

“Students learn to explain the concept of a mass defect using Einstein’s equivalence between mass and energy” (syllabus)

 

In a nuclear reaction the sum of the masses of the reactants is usually greater than the sum of the masses of the products. (There are some endothermic nuclear reactions where the opposite is true) The missing mass has been converted to energy. The amount of energy can be determined by Einstein’s equation: E = mc2

This can be illustrated by the fusion of two deuterium nuclei to form an isotope of helium and a neutron. The masses in atomic mass units are:

             = 2.01410u

             = 3.01603u

               = 1.00867u

The reaction is represented by the following equation.

                +       à   +

The sum of the masses of the reactants is 2.01410u + 2.01410u = 4.02820u

The sum of the masses of the products is 3.01603u + 1.00867u = 4.02470u

The loss of mass (mass defect) is 4.02820u - 4.02470u = 0.00350u

The energy released = 0.00350 x 931.5 = 3.26 Mev = 5.22 x 10-13 J

 

 

“Students learn to describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942” (syllabus)

 

 

 

Upon the discovery of fission, by Hahn and Strassmann early in 1939, he immediately saw the possibility of emission of secondary neutrons and of a chain reaction. He proceeded to work with tremendous enthusiasm, and directed a classical series of experiments which ultimately led to the atomic pile and the first controlled nuclear chain reaction. This took place in Chicago on December 2, 1942 - on a squash court situated beneath Chicago's stadium. He subsequently played an important part in solving the problems connected with the development of the first atomic bomb (He was one of the leaders of the team of physicists on the Manhattan Project for the development of nuclear energy and the atomic bomb.) Copied from http://www.nobel.se/physics/laureates/1938/fermi-bio.html

 

Fermi’s own account is given on http://hep.uchicago.edu/cp1.html

 

“Students learn to compare requirements for controlled and uncontrolled nuclear chain reactions. ” (syllabus)

 

Nuclear reactions produce a lot of energy. This can be released all at once such as in a nuclear bomb or over an extended period of time such as in a nuclear reactor.  The secret to controlling the rate of a nuclear reaction is to regulate the rate at which free neutrons collide with fissionable nuclei. This is done by using a material such as cadmium to absorb excess neutrons.

In a nuclear reactor the neutron absorbing material is made into control rods that are inserted in between the fuel rods to regulate the rate of the nuclear reaction. To speed the reaction up some control rods are removed from in between the fuel rods while to slow it down, more control rods are inserted between the fuel rods.

 

“Students perform a first-hand investigation or gather secondary information to observe radiation emitted from a nucleus using Wilson Cloud Chamber or similar detection device” (syllabus)

 

historical intro;

http://www.sciencemuseum.org.uk/on-line/electron/section3/1911b.asp

 

cloud chamber for cosmic rays

http://www.ulg.ac.be/masc/cloudchamber.htm

 

 

 

“Students solve problems and analyse information to calculate the mass defect and energy released in natural transmutation and fission reactions.” (syllabus)

 

Q. Tritium, an isotope of hydrogen with two neutrons, emits a beta particle to become helium.

                          à  +

Masses are:      = 3.01605u                     CHECK  DATA

                         = 3.01603u

                          = 0.00055u

Calculate the mass defect and binding energy.

 

A.        Mass defect = 3.01605 – 3.01603 – 0.00055 =   -0.00053u

            Energy = 0.00053 x 931.5 = 0.494 Mev = 7.9 x 10-14 J absorbed

 

 

Q.An example of a nuclear fission reaction is shown below.

92U235 + 0n1           92U236               57La148 + 35Br85 + 3 0n1

The masses of the atoms are;

92U235 = 235.044u

57La148 = 147.915u

35Br85 = 84.911u

0n1 = 1.009u

1 u = 1.66 x 10-27 kg.

(i)                 What is the mass defect of the reaction in atomic mass units per fission?

(ii)               What is the mass defect of the reaction in kilograms per fission?

(iii)             What is the energy released, in joules, by the fission of one atom of 92U235?

(iv)             What is the energy released, in MeV, by the fission of one atom of 92U235?

A.(i)             Mass on left = 235.044 + 1.009 = 236.053u

  Mass on right = 147.915 + 84.911 + 3(1.009) =235.853u

  Mass defect = 236.053 – 235.853 = 0.200u

(ii)      0.200 x 1.66 x 10-27 = 3.32 x 10-28 kg.

(iii)       E = mc2 = 3.32 x 10-28 (3x108)2 = 2.988 x 10-11 J

(iv)       0.200 x 931.5 = 186.3 Mev.

 

 

“4. An understanding of the nucleus has led to large science projects and many applications.” (syllabus)

 

“Students learn to explain the basic principles of a fission reactor” (syllabus)

A nuclear fission reactor enables a nuclear fuel such as uranium or plutonium to undergo fission (splitting of the nucleus) in a controlled manner with the release of energy. A diagram illustrating the core of a nuclear reactor is shown below.

 

The core of a nuclear reactor

A suitable fuel for the reactor would be enriched uranium.

Enriched uranium is uranium with a higher percentage than normal of the U-235 isotope. Naturally occurring uranium consists of about 99.3% U-238 and about 0.7% U-235 and traces of other uranium isotopes. This low percentage of U-235 is too low to sustain a chain reaction so physical separation techniques are used to remove some of the U-238 and leave a residue with about 3% U-235 and 97% U-238.

The uranium-235 will undergo fission in the reactor core and release energy.

Several equations are possible since U-235 does not always fission in the same way. Here are some examples;

 

92U235 + 0n1 à 92U236 à 57La148 + 35Br85 + 3 0n1

92U235 + 0n1 à 92U236 à 56Ba141 + 36Kr92 + 3 0n1

92U235 + 0n1 à 92U236 à 50Sn127 + 42Mo104 + 5 0n1

 

1.                  A chain reaction is a self-sustaining nuclear reaction in which enough neutrons are released to fission more atoms and keeps the reaction going.

2.                  The moderator slows the neutron so that it can be captured by the nucleus of the fissile material rather than bouncing off.

3.                  Heavy water or graphite are suitable moderators.

4.                  Control rods regulate the rate of the nuclear reaction by absorbing excess neutrons. To speed the reaction up some control rods are removed from in between the fuel rods while to slow it down, more control rods are inserted between the fuel rods.

5.                  Cadmium is a suitable material for control rods.

6.                  The coolant lowers the temperature of the reactor core and transfers heat from the core to where it can do useful work.

7.                  Light water or heavy water are suitable coolants. Heavy water is usually preferred as it can also be used as the moderator.

8.                  Workers are protected from radiation by a thick layer of reinforced concrete around the reactor core. This is often surrounded by lead to provide further protection.

 

 

 

“Students learn to describe some medical and industrial applications of radio-isotopes.” (syllabus)

 

Medicine:

Technetium-99 is used in diagnostic medicine. It is either injected into the bloodstream or consumed. It emits low-energy gamma rays that are easily detected outside the body.

Cobalt-60 emits high-energy gamma rays that are used to treat some forms of cancer. The cancer is bombarded with gamma rays from different directions so that there is maximum exposure of the cancerous cells to the radiation and less exposure of the healthy tissue surrounding the cancer.

 

Industry:

Cobalt-60 can be used to ensure uniform thickness of sheet metal. A cobalt-60 source is situated above the sheet metal as it rolls along the mill. It emits gamma rays that penetrate the metal and are detected by a geiger counter below. Variations in the thickness of the metal are detected as variations in the radiation count.

 

 

“Students learn to describe how neutron scattering is used as a probe by referring to the properties of neutrons” (syllabus)

 

Neutron scattering involves the interaction of neutrons with matter, and investigation of their subsequent path.  Scattering can be elastic, in which case diffractometers are used to study the structure of matter, or inelastic, in which case spectrometers are used to analyse the motion and energy of matter.

Neutrons have no electric charge so are unaffected by the charge on the nucleus or its surrounding electrons. Also their small deBroglie wavelength makes them ideal for studying the structure of matter.

 

 

“Students learn to identify ways by which physicists continue to develop their understanding of matter, using accelerators as a probe to investigate the structure of matter” (syllabus)

 

The linear accelerator consists of a series of tubes (called drift tubes) in a vacuum. The tubes are connected to high voltage, high frequency, alternating current; alternate tubes to opposite terminals of the A.C. When a charged particle enters the first tube it drifts through it because the electric field strength inside a hollow conductor is zero. When it reaches the gap between the tubes, it is subjected to a high potential difference and accelerates across the gap. It then enters the second tube where it drifts until it reaches the gap between the next two tubes. While it is drifting, the polarity of the tubes changes so that the potential difference between the tubes is always accelerating the particles in the one direction. As the particle moves from one tube to the next it gets faster. To synchronise with the A.C. it must spend the same time in each tube. This is achieved by making the tubes longer as the particle progresses along the linear accelerator.

      

 

 

 

       The cyclotron is more compact than the linear accelerator. It consists of two D shaped chambers connected to a high voltage, high frequency source of A.C. The chambers are in a vacuum and a strong magnetic field. The charged particle enters near the centre of the cyclotron and is accelerated across the gap by the potential difference between the chambers. The magnetic field then deflects the charged particle in a semi-circular path inside the chamber until it again reaches the gap between the chambers. While the particle is in the chamber the polarity of the A.C. between the chambers changes so that the charged particle is always accelerated (not decelerated) between the gaps. It accelerates across the gap twice with each revolution and after many revolutions it emerges with a very high energy.

                             

 

 

“Students learn to discuss the key features and components of the standard model of matter, including quarks and leptons” (syllabus)

 

The first half of the 20th century saw the model of the atom arise whereby atoms consisted of a nucleus of protons and neutrons surrounded by orbiting electrons. To make things more complicated, positrons and neutrinos were discovered. Then with the development of particle accelerators a whole myriad of new particles was discovered.

Particles can be divided into three groups: (i) hadrons which experience a strong nuclear force between them (ii) leptons that do not experience the strong nuclear force and (iii) bosons which carry the force fields between other particles.

Hadrons are composed of quarks. There are two types;

(i)                 Baryons that have a half integer spin and obey the Pauli exclusion principle. They consist of three quarks. Protons and neutrons are baryons.

(ii)               (ii) Mesons that have zero or integer spin. They are composed of two quarks (actually a quark and an antiquark). They are unstable and decay in a small fraction of a second.

Leptons do not experience the strong nuclear force. They have half integer spins and obey the Pauli exclusion principle. Electrons and electron neutrinos are the most common leptons.

Bosons are particles that carry the force fields. The strong nuclear force that holds quarks together is facilitated by an exchange of gluons between the quarks. The electroweak force includes electric fields, magnetic fields and the weak nuclear force responsible for beta decay. This force is facilitated by an exchange of photons. The third force field is gravity and this is believed to be due to an exchange of gravitons. Gravitons are yet to be discovered.

 

The Pauli Exclusion Principle states that two particles cannot exist in the same quantum state. In the case of electrons, only two electrons can have the same energy level and if they do, they have opposite spins. Particles that obey the Pauli exclusion principle have half integer spins and are called fermions.

 

“Students gather, process and analyse information to assess the significance of the Manhattan Project to society” (syllabus)

 

The Manhattan Project was  the project that developed the atomic bomb during World War II.

 

The most profound effect on society was the death of several hundred thousand people in Hiroshima and Nagasaki as the result of the atomic bomb dropped on each and the massive destruction that resulted. However, some argue that dropping the bomb shortened the war and resulted in less people being killed than if the war had continued.

 

After the war America and Russia built up their nuclear arsenals and this led to the Cold War. Some argue that this constant threat of war made people feel unsafe while others argue that their governments possessing such powerful weapons and the missiles to launch them made them feel safer.

 

The Manhattan Project led to the increased knowledge and understanding of nuclear processes. This has enabled the technology to be used for peaceful purposes such as the production of electricity by nuclear power stations but with this comes the danger of nuclear accidents such as that at Chernobyl and the problem of disposing of nuclear wastes. It has also facilitated the development of nuclear isotopes used in medicine, industry and agriculture.

 

 

“Students identify data sources, and gather, process, and analyse information to describe the use of

-          a named isotope in medicine

-     a named isotope in agriculture

-           a named isotope in industry” (syllabus)

 

Medicine:

Technetium-99 is used in diagnostic medicine. It is either injected into the bloodstream or consumed. It emits low-energy gamma rays that are easily detected outside the body.

Cobalt-60 emits high-energy gamma rays that are used to treat some forms of cancer. The cancer is bombarded with gamma rays from different directions so that there is maximum exposure of the cancerous cells to the radiation and less exposure of the healthy tissue surrounding the cancer.

 

Agriculture:

Carbon-14 can be used to trace the pathways of biological reactions such as photosynthesis in agriculture. The plant is exposed to carbon dioxide made up of the carbon-14 isotope. By analysing different parts of the plant for carbon-14 it is possible to determine the pathway of carbon dioxide through the plant and to develop more efficient growth patterns.

 

Industry:

Cobalt-60 can be used to ensure uniform thickness of sheet metal. A cobalt-60 source is situated above the sheet metal as it rolls along the mill. It emits gamma rays that penetrate the metal and are detected by a geiger counter below. Variations in the thickness of the metal are detected as variations in the radiation count.

 

 

 

 

 

The following account is taken from http://hep.uchicago.edu/cp1.html

 

Fermi's Own Story

By Enrico Fermi


It is ten years since man first achieved a self-sustaining atomic reaction.

Many people link this event only with the development of the atomic bomb and the subsequent efforts to develop the hydrogen bomb, reference to which has been made in the last few days by the Atomic Energy Commission.

The history of the first self-sustaining nuclear chain reaction, like that of all scientific achievements, begins with man¹s first philosophical speculations about the nature of the universe. Its ultimate consequences are still unpredictable.

The sequence of discoveries leading to the atomic chain reaction was part of the search of science for a fuller explanation of nature and the world around us. No on e had any idea or intent in the beginning of contributing to a major industrial or military development.

A partial list of the main stepping-stones to this development indicates many countries contributed to it.

The story begins in Paris in 1896 when Antoine Henri Becquerel discovered the existence of radioactive elements; that is, elements which spontaneously emit invisible, penetrating rays. Two years later, also in Paris, Pierre and Marie Cure discovered radium, for many years the best known of the radioactive elements.

In Zurich, Switzerland, in 1905, Albert Einstein announced his belief that mass was equivalent to energy. This led to speculation that one could be transformed into the other.

A most important discovery came in 1912 when Ernest Rutherford discovered the minute but heavy nucleus which forms the core of the atom. In ordinary elements this core is stable; in radioactive elements it is unstable.

Shortly after World War I, the same Rutherford achieved for the first time the artificial disintegration of the nucleus at the center of the nitrogen atom.

During the next decade, research progressed steadily, if unspectacularly. Then, in 1932, came a series of three discoveries by scientists working in three different countries which led to the next great advance.

Walter Bothe in Germany, and Frederic Joliot-Curie in Paris prepared the ground work that led James Chadwick of England to the discovery of the neutron. The neutron is an electrically neutral building block of the nuclear structure. The other build block is the positively charged proton.

The next step was taken in Rome in 1934. In experiments in which I was concerned it was shown that these neutrons could disintegrate many atoms, including those of uranium. This discovery was to be directly applied in the first atomic chain reaction eight years later.


The Discovery of Fission

The final stepping-stone was put in place in Berlin when Otto Hahn, working with Fritz Strassman, discovered fission or splitting of the uranium atom. When Hahn achieved fission, it occurred to many scientists that this fact opened the possibility of a form of nuclear (atomic) energy.

The year was 1939. A world war was about to start. The new possibilities appeared likely to be important, not only for peace but also for war.

A group of physicists in the United States‹including Leo Szilard, Walter Zinn, now director of Argonne National Laboratory, Herbert Anderson, and myself‹agreed privately to delay further publications of findings in this field.

We were afraid these findings might help the Nazis. Our action, of course, represented a break with scientific tradition and was not taken lightly. Subsequently, when the government became interested in the atom bomb project, secrecy became compulsory.

Here it may be well to define what is meant by the "chain reaction" which was to constitute our next objective in the search for a method of utilizing atomic energy.

An atomic chain reaction may be compared to the burning of a rubbish pile from spontaneous combustion. IN such a fire, minute parts of the pile start to burn and in turn ignite other tiny fragments. When sufficient numbers of these fractional parts are heated to the kindling points, the entire heap bursts into flames.

A similar process takes place I an atomic pile such as was constructed under the West Stands of Stagg Field at The University of Chicago in 1942.

The pile itself was constructed of uranium, a material that is embedded in a matrix of graphite. With sufficient uranium in the pile, the few neutrons emitted in a single fission that may accidentally occur strike neighboring atoms, which in turn undergo fission and produce more neutrons.

These bombard other atoms and so on at an increasing rate until the atomic "fire" is going full blast.

The atomic pile is controlled and prevented from burning itself to complete to complete destruction by cadmium rods which absorb neutrons and stop the bombardment process. The same effect might be achieved by running a pipe of cold water through a rubbish heap; by keeping the temperature low the pipe would prevent the spontaneous burning.

The first atomic chain reaction experiment was designed to proceed at a slow rate. In this sense it differed from the atomic bomb, which was designed to proceed at as fast a rate as was possible. Otherwise, the basic process is similar to that of the atomic bomb.

The atomic chain reaction was the result of hard work by many hands and many heads. Arthur H. Compton, Walter Zinn, Herbert Anderson, Leo Szilard, Eugene Wigner and many others worked directly on the problems at The University of Chicago. Very many experiments and calculations had to be performed. Finally a plan was decided upon.

Thirty "piles" of loss than the size necessary to establish a chain reaction were built and tested. Then the plans were made for the final test of a full-sized pile.

The scene of this test at The University of Chicago would have been confusing to an outsider‹if he could have eluded the security guards and gained admittance.

He would have seen only what appeared to be a crude pile of black bricks and wooden timbers. All but one side of the pile was obscured by a balloon cloth envelope.

As the pile grew toward its final shape during the days of preparation, the measurement performed many times a day indicated everything was going, if anything, a little bit better than predicted by calculations.


The Gathering on the Balcony

Finally, the day came when we were ready to run the experiment. We gathered on a balcony about 10 feet above the floor of the large room in which the structure had been erected.

Beneath us was a young scientist, George Weil, whose duty it was to handle the last control rod that was holding the reaction in check.

Every precaution had been taken against an accident. There were three sets of control rods in the pile. One set was automatic. Another consisted of a heavily weighted emergency safety held by a rope. Walter Zinn was holding the rope ready to release it at the least sign of trouble.

The last rod left in the pile, which acted as starter, accelerator and brake for the reaction, was the one handled by Weil.

Since the experiment had never been tried before, a "liquid control squad" stood ready to flood the pile with cadmium salt solution in case the control rods failed. Before we began, we rehearsed the safety precautions carefully.

Finally, it was time to remove the control rods. Slowly, Weil started to withdraw the main control rod. On the balcony, we watched the indicators which measured the neutron count and told us how rapidly the disintegration of the uranium atoms under their neutron bombardment was proceeding.

At 11:35 a.m., the counters were clicking rapidly. Then, with a loud clap, the automatic control rods slammed home. The safety point had been set too low.

It seemed a good time to eat lunch.

During lunch everyone was thinking about the experiment but nobody talked much about it.

At 2:30, Weil pulled out the control rod in a series of measured adjustments.

Shortly after, the intensity shown by the indicators began to rise at a slow but ever-increasing rate. At this moment we knew that the self-sustaining reaction was under way.

The even was not spectacular, no fuses burned, no lights flashed. But to us it meant that release of atomic energy on a large scale would be only a matter of time.

The further development of atomic energy during the next three years of the war was, of course, focused on the main objective of producing an effective weapon.

At the same time we all hoped that with the end of the war emphasis would be shifted decidedly from the weapon to the peaceful aspects of atomic energy.

We hoped that perhaps the building of power plants, production of radioactive elements for science and medicine would become the paramount objectives.

Unfortunately, the end of the war did not bring brotherly love among nations. The fabrication of weapons still is and must be the primary concern of the Atomic Energy Commission.

Secrecy that we thought was an unwelcome necessity of the war still appears to be an unwelcome necessity. The peaceful objectives must come second, although very considerable progress has been made also along those lines.

The problems posed by this world situation are not for the scientist alone but for all people to resolve. Perhaps a time will come when all scientific and technical progress will be hailed for the advantages that it may bring to man, and never feared on account of its destructive possibilities.


From The First Reactor, Published December, 1982 by the U.S Department of Energy

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