CARESA TRIAL 2 – ANSWERS

 

1.D      2.C      3.A      4.B      5.A      6.C      7.D      8.D      9.B      10.D    11.A

 

12.D    13.D    14.C    15.B

 

16. (i) ½ mv² + -Gmm_E/r >0                ½ v² –Gm_E/r >0           v² > 2Gm_E/r

            G = 6.67 x 10^-11 Nm²kg^-2         m_E = 6.0 x 10²⁴ kg       r = 6.38 x 10⁶ m

            v² > 2 x 6.67 x 10^-11 x 6 x 10²⁴/ 6.38 x 10⁶      = 12544000

            v > 11200 ms^-1

(ii) v_y² = u_y² + 2 a_y Dy        11200² = 0² + 2 a_y 100            a_y = 11200² / 200

      a_y = 6.27 x 10⁵ ms^-2

(iii) No. An object fired from Earth would either escape from the Earth’s gravity as the gravity from other celestial bodies has a greater influence or would go into an elliptical orbit passing through its launching point.

(iv) The method would not be suitable for manned spacecraft as the acceleration and hence the “g” forces would be far greater than humans could withstand.

17.       mg = Gm₁m₂ /d²          g = Gm/d²

            The gravity at the surface of the red giant would be 1/(100²) that at the surface of a main sequence star of the same mass i.e. 1/10000 or 10^-4

18.

                                   

19. (i) Experiments had indicated that light is a wave and it was thought that light waves would need a medium to travel through. The aether was thought to be this medium.

      (ii) M & M used a half silvered mirror at a 45^o angle to split a ray of light into two rays traveling at right angles to each other. These two rays were reflected by plane mirrors and recombined in an interferometer that recorded the interference patterns formed by the recombined light rays. The entire apparatus was situated on a large sandstone disk floating in mercury. The apparatus was rotated 90^o so that the ray traveling parallel to the aether would now be traveling at right angles and vice versa. This would cause a change in the interference patterns. No such change was observed.

     (iii) Since the aether could not be detected then it would not affect the speed of light. This led to the assumption that the speed of light is constant and was the basis for Einstein’s relativity theories.

20.       (i)         8.4 /10 = 0.84c

            (ii)  t_o = t_v \/(1 – v²/c²)  t_o = 10\/(1 – 0.84²) = 10\/(0.2944)       t_o = 5.43 years

21.       When the motor is starting there is no back emf. This means that the supply emf is now the net emf and this higher voltage causes more current to flow through the coil of the motor. The increase in current can cause the motor to burn out. As the motor reaches its operating speed, the back emf increases causing the net emf, and consequently the current, to fall to levels that will not damage the motor.

22.              A soft iron core was constructed by winding some iron wire into a loop of about 20 turns and about 10 cm diameter. A length of insulated wire was wound around one side of the loop 20 times to create the primary coil. This was connected in series to a switch and the A.C. terminals of a power pack. An A.C. voltmeter was connected in parallel across the ends of the primary coil. The secondary coil was constructed by winding a length of insulated wire 100 times around the other side of the loop of iron wire. The ends of the secondary coil were connected to the terminals of an A.C. voltmeter. When the primary circuit was switched on an alternating current of higher voltage was recorded in the secondary circuit. Low voltages and low currents were used in the primary coil to minimize the danger of electric shock. The experiment was also carried out on a side bench, well away from water, to eliminate the danger of water entering the power pack from a wet bench and increasing the risk of electrocution. The experiment was carried out on a heatproof mat to minimize the risk of someone burning themselves as the soft iron core heated up due to eddy currents.

23.               

24.       (i) Slip rings transfer the alternating current, via the brushes, to the external circuit. The split-ring commutator changes the direction of the current to the external circuit at the same rate as the direction of the current is changing in the coil. This means that direct current is supplied to the external circuit.

(ii) The brushes transfer the current from the commutator or slip rings to the external circuit.

 

 

 

25.       Soon after the industrial revolution, wood and later coal and coke were used to fire steam engines for industry. The resulting smoke made cities dirty and unhealthy. With the development of the A.C. generator steam engines were replaced by electric motors and the amount of direct combustion in the cities decreased greatly. The result was cleaner and healthier cities and towns. However there are still environmental problems in producing the electricity. While filters remove some of the pollutants there are still problems with fine particles, gases producing acid rain and carbon dioxide, a greenhouse gas produced by burning fossil fuels. With the huge worldwide demand for electricity the production of greenhouse gases and the consequent global warming has become a serious problem. While hydroelectricity produces no atmospheric pollutants it requires dams with large storage areas. This destroys large regions of flora and fauna upstream from the power station as well as interfering with the natural flow of the river. While the A.C. generator has been a benefit to society it appears that the future will require that it is powered by more environmentally friendly methods such as wind power or that it be replaced by solar cells.

 

26.       Thermionic devices such as the diode and triode valves were brittle and bulky so scientists sought alternatives that would do the job better. Research into semiconductors led to the development of the germanium diode and germanium based transistors. Although these were an improvement on thermionic devices they tended to break down in hot conditions. Germanium was favoured over silicon at the time because technology had not been developed that would produce silicon in sufficiently pure form for solid-state use. However as methods of purifying silicon were developed this became the preferred semiconductor for solid-state devices because it retained its semiconducting properties at higher temperatures than germanium. As research into crystal growth and etching techniques were developed scientists were able to miniaturize components and develop the integrated circuit where hundreds of transistors and other components are included in a chip that is smaller than a fingernail.

27                (i) E = hf = hc/l = 6.626 x 10^-34 x 3 x 10⁸/300 x 10^-9 = 6.626 x 10^-19 J.

(ii)        (a) The number of photoelectrons and hence the photocurrent would increase.

(b) The kinetic energy of the photoelectrons would increase. This would require a higher stopping voltage.

28.              The Braggs shone x-rays onto the nickel surface and found that at certain angles they could produce diffraction patterns. By applying the equation; 2d sinq = nl (Bragg’s Law), they were able to determine the spacing between atoms in a crystal.

29.              The electrodynamic system used in Japan uses superconductors to provide magnetic levitation for the maglev train. This uses the opposing forces between the superconducting magnets on the train and the conventional magnetic coils in the guideway to levitate the train and reduce friction.. To propel the train along the track there are propulsion coils in the guideways. The alternating current in the guideways produces a changing magnetic field that alternately pushes and pulls the train along the track.

 

30.              BCS stands for Bardeen, Cooper & Schrieffer; the first letters of the surnames of John Bardeen, Leon Cooper and John Schrieffer who developed the model to explain how superconductivity works.

An electron moving through a superconductor will cause the lattice to distort and will induce vibrations. The distortion of the crystal lattice emits a phonon i.e. a photon of vibrational energy, and this forms a region of positive charge behind the electron. This attracts the electron behind it to form a pair known as a Cooper pair. There is a transfer of a phonon from the first to the second electron and it is this transfer of phonon energy that keeps the Cooper pairs together. They are not permanent bonds and Cooper pairs keep breaking up and reforming.

 

31.       Metals consist of a lattice of positive ions with the valency electrons delocalised i.e. free to move throughout the lattice. The electrons are usually in constant random motion between the ions but in the presence of an electric field will drift in the opposite direction of the electric field to produce a current.

 

32.       An n-type semiconductor consists of silicon or germanium that has been doped by adding a small amount of a group 5 element such as arsenic. Four electrons of the group 5 element bond with the four valency electrons of the silicon or germanium while the fifth valency electron of the dopant is easily mobilised to become the current. A p-type semiconductor consists of silicon or germanium that has been doped by adding a small amount of a group 3 element such as gallium. The three valency electrons of the group 3 element bond with three of the electrons of the silicon or germanium while the fourth valency electron of the silicon or germanium remains unbonded.  This unbonded electron represents a hole in the crystal lattice and is similar to a positive charge since it attracts electrons. As an electron is attracted from a nearby atom to fill the hole it forms a hole i.e. electron deficiency in the donor atom which attracts an electron from another nearby atom and so on. In this way the holes act as the primary charge carriers and drift in the opposite direction to electron flow. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ASTROPHYSICS

33. (a) Craters, Mountains

(b) The movement of the atmosphere and the variation of its density at different heights and temperatures decreases the resolution of ground-based telescopes. The selective absorption of E.M. radiation by the atmosphere restricts observations to the visible and radio bands.

(c) d = 1/p             p = 1/d = 1/120 = 8.3 x 10^-3 seconds

(d) A spectrum is a wave that has been separated into its component wavelengths. A continuous spectrum has all wavelengths present e.g. a rainbow.  While all wavelengths are present in a continuous spectrum they are not of equal intensity. A blackbody emits a continuous spectrum with the most intense wavelength depending on the temperature of the body. A line spectrum is black except for a few lines of characteristic wavelengths.

An emission spectrum consists of the wavelengths emitted by a low-pressure gas that is in an excited state because energy has been put into it. It arises from electrons returning from a high-energy state to a low energy state. Low-pressure gases in an excited state produce an emission line spectrum. Heated solids and high-pressure gases produce a continuous emission spectrum.

An absorption spectrum is formed when a continuous spectrum shines through a gas that is cooler than the continuous spectrum source. The gas absorbs energy at its characteristic wavelengths and re-radiates it in all directions. It transmits other wavelengths of the continuous spectrum so that the result is a continuous spectrum with black stripes.

(e) By measuring magnitudes at two different wavelengths it is possible to determine the temperature of a star. Photographic emulsions are most sensitive to blue light so the photographic magnitude is written as m_B or more commonly just as “B”. The human eye is most sensitive to yellow light so the visual magnitude is written as m_V or more commonly just as “V”. The difference between the two magnitudes B - V is called the colour index. The temperature of a star can be determined by determining its colour index.

(f) The star would be a spectroscopic binary. If the two spectra are present at the same time then this is consistent of a pair of stars of the same spectral class orbiting each other so that the one receding from Earth shows a red shift while the one approaching Earth shows a blue shift. If the two spectra alternate then this is consistent with a star orbiting an unseen companion such as a neutron star or black hole. The star would exhibit a blue shift as it was approaching Earth and a red shift as it was receding.

(g) The apparent magnitude of the star is determined by photometry and spectroscopy is used to determine its spectral properties and class. The spectral class is located on the horizontal axis of the H.R. diagram. By drawing a vertical line to the appropriate star group and then drawing a horizontal line to the vertical axis, the absolute magnitude can be determined. Since we now know both the apparent and absolute magnitudes we can use the distance modulus to determine the distance to the star.

(h) a. 2.512^{1.26 – 0.9} = 2.512^0.36 = 1.39 times as bright

      b. M = m - 5 log d/10 M = 0.9 - 5 log 80/10  = 0.9 – 5 log8 = 0.9 – 5 x 0.9

= -3.6

 

 

 

 

(i) Open clusters consist of young stars while globular clusters consist of old stars.

      Open clusters consist of up to 1000 stars while globular clusters contain up to 1000000 stars.

      Open cluster stars have high heavy metal concentrations (they are second or third generation stars) while globular cluster stars have low heavy metal concentrations (they are first generation stars).

      Open clusters are found in the galactic plane while globular clusters are found in the galactic halo.

      Open clusters are irregular in shape while globular clusters are spherical.

(j) All of the stars in a globular cluster would have been formed at the same time. The time that a star spends on the main sequence of the HR diagram depends on its spectral class i.e. its size. The larger the star, the less time it spends on the main sequence. The age of a globular cluster is the age of the stars on the main sequence and this is equal to the total life expectancy of the largest stars still on the main sequence.

 

 

 

FROM QUANTA TO QUARKS

34. (a) Both the Bohr and the Rutherford model had electrons orbiting a central, positive nucleus.

(b) Bohr proposed that electrons could only orbit in certain fixed orbits, where they were stable and would not emit radiation. Furthermore they could absorb a fixed amount of energy to orbit in a higher energy level. However the higher energy level would be unstable and the electron would emit a fixed amount of energy (a photon) and return to its lower energy state.

(c) 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.

(d)

Component	Function	Suitable Material
Fuel Rods	Provide fissionable material	Enriched uranium
Moderator	Slows neutrons so they can be captured by nucleus.	Heavy water
Control Rods	Absorb excess neutrons to control rare of reaction.	Cadmium
Coolant	Transfers heat to where it can do useful work.	Water or heavy water

 

(e) ₈₈Ra²²⁶  à ₈₆ Rn²²² + ₂He⁴

      Mass on left = 226.09600     Mass on right = 222.08690 + 4.00260 = 226.0895

      Mass defect = 226.09600 – 226.08950 = 0.0065 u.

      Energy released = 0.0065 x 931.5 = 6.05 MeV

 

Quanta to Quarks (continued)

 

(f) Fertilisers containing phosphorus-32 or nitrogen-15 can be added to the soil to trace the uptake mechanisms of roots and foliage. This can reveal the most efficient times and methods for applying the fertiliser  to maximize its results.

(g) Diffraction refers to the spreading out of a wave as it passes around the edge of an object or when it passes through a small gap.

(h) They reflected electrons off the surface of a nickel crystal and examined the scattering of the reflected electrons. They found that certain angles produced interference patterns of maximum concentration and other angles showed minimum concentration. These patterns were similar to the X-ray diffraction patterns discovered by the Braggs a few years earlier and indicate that electrons have a wave nature.

(i)     De Broglie proposed the wave-particle duality theory i.e. all waves show some properties of particles and all particles show some properties of waves.

(j) De Broglie proposed that stable orbits consist of a whole number of wavelengths of the electrons. This could only occur if electrons had a wave nature.

(k) The Manhattan project was the wartime project that developed the atomic bomb. While the bomb killed hundreds of thousands and destroyed the cities of Hiroshima and Nagasaki it is also claimed that it saved lives by shortening World War II.

      The availability of nuclear weapons and the tensions between America and Russia led to the “cold war” between these two superpowers as each tried to intimidate the other by the development and testing of bigger and more deadly nuclear weapons. While some argue that the potential for such a war with its catastrophic consequences for the human race would cause a state of anxiety throughout society others argue that the fact that both sides had such weapons would instil a sense of confidence that these weapons would not be used through fear of retaliation.

The technology of the Manhattan project led to the development of the controlled nuclear reaction and the nuclear reactor. This has enabled nuclear reactions to be used for energy production and the production of radioisotopes used in medicine. While there are many benefits of the nuclear reactor these have to be weighed against the problems of disposing of nuclear waste and the possibility of a nuclear meltdown.

While it may be argued whether the Manhattan Project has had a positive or negative impact on society it seems certain that it has changed society. Governments are now responsible for major decisions regarding the application of nuclear technology as a direct result of the Manhattan Project.