HCI P2 6
(a) The tip of a Scanning Tunnelling Microscope (STM) probe is positioned at a distance d above a sample surface which has an energy difference, U - E of 6.0 eV between the potential barrier’s height and the most energetic electrons at its surface. (i)
Calculate the value of d at which the tip-surface transmission coefficient T is 0.0001. 0.368 [2]
(ii)
Suppose d decreases by 1 %, calculate the percentage change in transmission coefficient, T. 9.66 or 9.73 % [2]
(b) Explain how the STM maintained at a fixed vertical position is used to obtain atomic scale images. [2] 7
This question is about the homopolar generator. In principle, a homopolar generator consists of a conducting disc spinning about an axis in a magnetic field parallel to this axis. When the spinning disc is stopped suddenly, all its kinetic energy can be used to generate a large current surge. In order to spin the disc, a d.c. power supply is connected as shown in Figure 7.1. The magnetic force on the disc due to the current passing from the axle to the rim of the conducting disc provides the necessary accelerating force. As the conducting disc speeds up, however, there is an increasing voltage generated across the terminals T1 and T2. When the power supply is disconnected, this voltage can be used to drive a current through a resistor connected between them as shown in Figure 7.2.
Figure 7.1
Figure 7.2
1
The magnitude of the voltage V can be calculated from the relationship V = π (rd2 − ra2 )kB where rd and ra are the radii of the disc and axle respectively, and B is the magnetic flux density, assumed to be uniform over the surface of the disc. The homopolar generator is used as a research tool to produce a huge surge of current when their terminals are suddenly short-circuited. One large homopolar generator in Australia, which is designed to produce a large current surge, measures 3.6 m in diameter, rotates at 15 Hz and is so massive that the kinetic energy it stores at this speed is 580 MJ. When it is short-circuited, the current surge is used to produce shortlived but extremely high magnetic fields in order to study the properties of matter under extreme conditions. It is proposed that such fields could be used in an electromagnetic gun to project a small mass to speeds of over 7 km s-1. This speed is of the order of the speed of satellites in low orbits and hence the projected masses could be used to study the problems encountered by missiles re-entering the atmosphere. [1]
(a)
What is meant by the term “short-circuited” as used in the passage?
(b)
(i)
Explain why there is an increasing voltage generated between terminals T1 and T2 when the conducting disc speeds up. (Paragraph 3) [2]
(ii)
Is the output of a homopolar generator a.c. or d.c.?
(iii)
Give two applications which are suggested in the passage for the huge surges of current produced by a homopolar generator. [2]
(c)
[1]
Figure 7.3 shows a current surge from a short-circuited homopolar generator.
Figure 7.3 (i)
Estimate the charge that flows during this surge. 2.4 – 3.1 MC
[3]
(ii)
Calculate the maximum power dissipated when the terminals T1 and T2 of the generator, which has an internal resistance of 0.12 mΩ, are connected [1] together through a negligible external resistance. 3.3 x 108 W
2
(d)
Using V = π (rd2 − ra2 )kB , determine the units for k. Hence, suggest what physical [3] quantity may be represented by the symbol k. -1 s
(e)
Describe the energy transformations that take place in the process shown in (i)
Figure 7.1
[1]
(ii)
Figure 7.2
[1]
HCI P3 2 (a) Define the tesla. 1 Tesla is a unit of the magnetic flux density of a magnetic field if the force acting per unit length on an infinitely long conductor carrying a current of 1 A and placed perpendicular to the magnetic field is 1 N m-1.
[1]
(b) At the equator, a thin coil of 50 turns and of diameter 10.0 cm is in a vertical plane (with axis in the East-West direction) as shown in Figure 2.1. A compass, which is in a horizontal plane, has its pivot coinciding with the centre of the coil. Initially, no current flows through the coil and the compass is pointing North as shown.
µ0 NI , 2R where I represents the current, N the number of turns of coil and R the radius of the coil. The Earth’s magnetic field is 50.0 µT. The magnetic flux density at the centre of a thin coil follows the formula B =
N W
E S
Figure 2.1 When a current of 100 mA flows in a clockwise direction as viewed from the West, determine (i) the magnetic flux density, Bc, and its direction at the centre of the coil, due only to the current flowing in the coil.6.3 x 10-5 T East [2]
3
(ii)
(c)
the resultant magnetic flux density at the centre of the coil, BR, and the new [2] direction (angle θ from the North) which the compass will be pointing. -5 8.0 x 10 T 51.6º
A powerful electromagnet produces a uniform field in the gap between its poles, each of which measures 4.00 cm × 4.00 cm and are facing each other. There is no field due to the electromagnet outside the gap. The circular coil in (b) is placed between the poles such that its plane is perpendicular to the field lines and encloses all the field lines, as shown in Figure 2.2.
4.00 cm
North pole of electromagnet
4.00 cm
South pole of electromagnet
Figure 2.2 The magnetic field produced by the electromagnet is adjusted so that the field strength steadily decreases from 0.40 T to zero in 0.50 s. Calculate the e.m.f. generated in the coil. [2] 0.064 V 4
Diodes used in rectifying alternating current to direct current are p-n junctions made of semiconductors. A p-n junction is formed when p-type and n-type extrinsic semiconductors are joined, as shown in Figure 4.1.
p
n
Figure 4.1 Figure 4.2 shows a sinusoidal power supply with a peak output of 3.0 V at a frequency of 50 Hz. The power supply is connected to a 68 Ω load resistor. The p.d. across the load resistor is displayed on an oscilloscope.
3.0V peak 50 Hz
68 Ω oscilloscope
Figure 4.2
4
(a)
Explain how the p-n junction acts as an open or closed switch in the circuit as the voltage varies. You may draw a diagram if you wish.
[4]
(b)
The oscilloscope is set to a voltage sensitivity of 1.0 V cm-1. The trace in Figure 4.3 is seen on the grids of the oscilloscope. Calculate the average power dissipated in the [3] load resistor. 2.4 V; 0.021 W 1 cm 1 cm
Figure 4.3 5
Figure 5.1 shows an experimental arrangement used to estimate the activity of a radioactive source which emits β-particles.
Geiger-Muller tube
670
source
counter
Figure 5.1
The following count-rates, as detected by the Geiger-Muller tube, are taken at two different times t. Note that background-count has been established to be 50 min-1. t / hour 0 6.0
count-rate / min-1 3248 851
0.80% of the β-particles leaving the source are recorded by the counter. Each β-particle produces a count of one. (a) Determine the activity of the source at the start of the experiment. 6600 Bq
[2]
5
(b) Determine the half-life of the source. 3.0 h
6
[2]
(c)
Counting is ended when the recorded count-rate falls to less than 100 min-1. Determine the time after the start of the experiment at which this occurs. [2] 18.0 h
(a)
(i)
1. What is meant by internal energy of a system?
[1]
2. Explain how the concept of internal energy is applied to an ideal gas as compared to a real gas. [2] (ii)
The following is an excerpt from American Scientific (May 2009):
Many of the gases that make up Earth’s atmosphere and those of the other planets are slowly leaking into space. This leakage explains many of the solar system’s mysteries. For instance, Mars is red because its water vapour got broken down into hydrogen and oxygen, the hydrogen moved at higher speeds and drifted away, and the remaining oxygen reacted with rocks to form rust, and gives Mars its characteristic red colour. Explain the following.
(b)
1. Hydrogen molecules are faster-moving than oxygen molecules.
[2]
2. Fast-moving molecules are able to escape.
[1]
3. Some oxygen molecules are also able to escape.
[1]
1.00 x 10-2 mol of neon gas is contained in a vessel capped by a light moveable piston. At equilibrium the volume enclosed by the vessel is 250 cm3. Take the mass of a neon atom to be 20.0 u and atmospheric pressure to be 1.01 × 105 Pa. Assume behaviour of the gas to be ideal.
> 2 c < ρ 13 = p
(i)
Using
, where p is the pressure of the gas, ρ is the density of
the gas, and is the mean-square speed, calculate the root-mean-square speed of the neon atoms. 616 ms-1 (ii)
The vessel is submerged in a pure ice-water mixture and allowed to come to thermal equilibrium with its surroundings. The piston settles at a new position, X.
6
[3]
Position X Ice and water
Figure 6.1
(iii)
1. Explain what is meant by thermal equilibrium.
[1]
2. Calculate the change in the volume of the gas in the vessel. - 25 cm3
[2]
The gas is subjected to a cycle of changes A→ B→ C→ A as shown in Figure 6.3. A→ B: The piston is quickly pushed down from position X to position Y. You can assume that this process takes place so quickly that there is no heat transfer with the surroundings. B→ C: The piston is held at position Y until the gas is again at the temperature of the ice-water mixture. C→ A: The piston is slowly raised back (such that there is ample time for heat transfer between the gas and its surroundings and there is no temperature change in the gas) to position X.
pressure B
X Y Ice and water
C A volume
Figure 6.2
Figure 6.3
1. The first law of thermodynamics can be expressed as ∆U = Q + W,
7
where ∆U is the increase in internal energy, Q is the heat supplied and W is the work done on the system. Complete the following table. Use ‘+’ to indicate a positive change in the quantity, a ‘−‘ to indicate a negative change in the quantity and ‘0’ to indicate no change in the quantity.
∆U
Q
W
A→ B: B→ C: C→ A:
Entire Cycle
[4]
2. The cycle is repeated many times. If 2.00 g of ice is melted by this action, calculate the total work done on the gas. Show your working clearly. Take the specific latent heat of fusion of ice to be 3.36 × 105 J kg-1.672 J [3] 7(c) Figure 7.2 shows the energy level diagram of a three-level laser. Lasing takes place between E2 and E1.
E3 E2
E1
Ground state Figure 7.2 (i)
State the unique characteristic of energy level E2 that is important in the operation of this laser. [1]
(ii)
Explain the general action of the laser represented by Figure 7.2 in terms of population inversion and stimulated emission. [4] Atoms in the ground state are excited to E3. These quickly de-excite to the upper laser level E2. When more atoms are in the upper laser level than in the ground 1 state (i.e. lower laser level), population inversion is produced between the upper and lower laser levels.
8
When a photon of energy equal to E2 – E1 passes through the laser 2 medium, it can either be absorbed to cause excitation from E1 to E2 or stimulate de-excitation from E2 to E1, releasing another photon of energy E2 – E1 in the process. With population inversion, deexcitation is more probable than absorption. Stimulated emission produces photons of the same phase, energy, frequency, polarization and direction of travel as the incident photon. The photons are sent back and forth in the laser medium (by mirror 1 reflection) and in the process they will cause more stimulated emissions. (iii)
Figure 7.3 shows the energy level diagram of a four-level laser. Lasing takes place between E3 and E2.
E4 E3
E2 E1
Ground state Figure 7.3
What is the advantage of the four-level laser over the three-level laser? Lower laser state is not ground state. After atoms move from the upper laser [1] level (E3) to the lower laser level (E2) through stimulated emission, they will quickly depopulate to the ground state (E1). This reduces the loss of photons by absorption between the upper (E3) and lower (E2) laser levels. 8 (a)
The radioactive isotope of Bismuth, 210 83 Bi decays into Polonium (chemical symbol: Po) with the emission of a beta particle. (i)
What is a beta particle?
[1]
(ii)
Write down the equation representing the beta decay of
(iii)
State two quantities that are conserved in any radioactive decay process.
(iv)
[2] The mass of a 210 83 Bi nucleus is 209.939 u. Show that its mass defect is 1.767 u. (mass of proton, mp = 1.00729 u; mass of neutron, mn = 1.00867 u )
(v)
Hence calculate the binding energy, in MeV, of 1646 MeV
210 83
210 83
[1]
Bi .
[2]
[2]
Bi .
9
(b)
James Chadwick, in some experiments conducted prior to World War I, used a Geiger Counter to study beta particles emitted from a source and deflected by a uniform magnetic field. He found that the beta particles had a wide range of radii of curvature in the field, indicating that the beta particles were emitted with a distribution of energies rather than with a distinct single value of energy. Figure 8.1 shows the energy spectrum for beta particles emitted during the decay of Bi-210. The intensity (vertical axis) indicates the number of beta particles emitted with each particular kinetic energy (horizontal axis).
Energy spectrum of beta particles emitted from 210Bi
Figure 8.1 (i)
1. Determine, from Figure 8.1 above, Q, the maximum possible energy of the beta particle emitted from 210 83 Bi . 1.2 MeV 2. Hence calculate the velocity of the beta particle. 6.5 x 108 ms-1 Comment on the value you obtained.
[1]
[2]
3. Using values in (b)(i)1. and (a)(iv), determine the mass of the resultant Polonium nucleus, in units of u, and express your answer to 3 decimal places. [3] 209.937 u
10
(ii)
From Figure 8.1, identify the most probable energy value for the beta particle to be detected with. [1] Range of values accepted : 0.16 - 0.18 MeV
(iii)
It is noted that for stable isotopes of heavy elements, there is an optimal neutron to proton ratio. Unstable isotopes of a particular element will undergo radioactive decay in order to achieve this optimal ratio. Suggest, with a reason, whether 210 83 Bi has an excess of neutrons or protons, as compared to the [2] optimal ratio.
(iv)
The continuous spectrum of kinetic energy values of the beta particle presented a problem to early physicists. Consider a stationary nucleus decaying into a beta particle and the daughter nucleus, and assume the daughter nucleus is in a stable state that does not emit any gamma particles. By considering the conservation of linear momentum and energy, explain how the continuous spectrum of beta particle energies gave rise to this problem. [2]
(v)
Suggest what was hypothesized by physicists to resolve the problem.
[1]
NJC P2 3
Fig. 3 below shows the energy levels of neon that are involved in the production of laser light from a helium-neon laser. Energy values are given relative to the ground state.
3.30 × 10-18 J 2.99 × 10-18 J Fig. 3
0J
Ground state
A photon of the laser light has energy 1.94 eV. 3(a)(i) Use an arrow to show on the figure above, the energy transition that produces the photon. [1] 3(a)(ii) Calculate the wavelength of the laser light. [2] 641 nm 3(b) For laser action, atoms of the element which produce the laser light must have a metastable state so that population inversion can occur. Laser light is then produced by stimulated emission. Explain the meaning of the terms in italics. [3] 3(b)(i) Population inversion
11
6
In the interior of the Sun, nuclear reactions take place whose net result is the conversion of hydrogen into helium with the release of energy. The three stages in this proton-proton cycle are as follows: reaction (1): reaction (2): reaction (3):
1 1 1 1 3 2
H +11H →12 H + +10 e H + 12H → 23 He + γ He+ 23He→ 24 He + 211H
The masses of the nuclei are: 1 2 3 4 1 H :1.00728u, 1 H :2.01355u, 2 He : 3.01493u, 2 He : 4.00151u. The mass of the positron
0 +1
e is 0.00055u.
For there to be two 23 He nuclei available for reaction (3), the first two reactions must take place twice. What is the total energy released in the creation of a single helium-4 nucleus from protons? [4] 3.96 x 1012 J 6(a)
6(b)
The first stage in the process is the fusion of two hydrogen nuclei. Why is energy needed to do this? [1]
6(c)
When hydrogen is raised to high temperatures, it dissociates into atoms and is ionized. Assuming that hydrogen ions behave like an ideal gas inside the Sun’s core, estimate the temperature required for the hydrogen ions to achieve an energy of 1.0 MeV in order for fusion to take place. [2]
3.87 x 109 K 6(d)
Why are these reactions sometimes called thermonuclear reactions?
[1]
NJC P3 4(a)
Describe one piece of evidence based on the observations from the photoelectric effect experiment to support the particulate nature of electromagnetic radiation when it interacts with matter. [2]
(b)
The stopping potential for electrons emitted from a metallic surface illuminated by light of wavelength 480 nm is 0.64 V. When the incident wavelength is changed to a new value, the stopping potential is 1.30 V.
Calculate (i) the work function for this metallic surface, 3.12 X 10-19 J (ii) the new wavelength. 383 nm
[2] [1]
12
(c)
A 1500 kg car moving at 25 ms-1 approaches a hill that is 40 m high and 30 m wide. The hill can be regarded as a potential barrier where the potential energy is gravitational. If the car were a matter wave approaching a potential barrier, calculate (i) the gravitational potential energy of the car at the top of the hill,[1] 5.89 x 105 J the transmission coefficient of the car, if it could tunnel through the hill. Leave your answer in terms of the exponential e. [2] 40 exp (- 1.08 x 10 ) (ii)
5
A spray can contains liquid paint with compressed gas in the space above it, as shown in Fig.5. Pressing down the cap opens a valve which allows the gas to expand, forcing paint through the nozzle. The cap is pressed until all the paint is expelled, leaving the can filled with gas at a pressure which is still greater than atmospheric.
(a) The can has an internal volume of 6.6 × 10-4 m3 and initially contains 5.0 × 10-4 m3 of paint. The gas in the can is at an initial pressure of 7.8 × 105 Pa. The pressure of the gas left in the can when all the paint has just been expelled is 1.9 × 105 Pa. Show that the expansion of the gas is approximately isothermal. State an assumption used in your calculation. (b)
1.
Define specific heat capacity.
Fig.5 [3] [1]
2. Describe an experiment in which the specific heat capacity of an unknown piece of metal of a certain mass could be determined with the use of an electrical heater of known power. [4] (c)
The line ABCD in the graph below is the indicator diagram for a particular engine.
13
A
B D
C
Explain whether thermal energy is taken in or given out by the engine for the process B. [3] - 9000 J
(i)
(ii) Determine the net work done by the engine during the cycle ABCD. [3] 20 kJ (iii)
The useful output power of the engine is equal to the rate of net work done by the engine. If the engine is running at 3 cycles per second, determine useful output power. [2]
60 kW (iv)
(iv)
This engine obtains its input energy from burning fuel of calorific value 34 MJ kg-1 at a rate of 2.4 × 10-2 kg s-1. Calculate the efficiency of the engine. 0.0735 [3] The line ABED in the graph is the indicator diagram for the same engine after a modification has been made. Without further calculation, compare the performance of the modified engine with that of the original engine when both engines are making the same number of cycles per second. [1]
14
A
B D
E
TJC P2 6
(a) (b)
Define binding energy of a nucleus. (i)
[1]
12 6
C and 136 C are two different isotopes of carbon. Calculate the binding energy per nucleon, in MeV, of the two isotopes, given the following data: mass of
12 6
mass of
1 0
C = 12.000000 u
n = 1.008665 u
mass of 11 H = 1.007825 u mass of 136 C = 13.003355 u 7.70 MeV; 7.49 MeV
(c)
(ii)
Hence, state and explain which of these two isotopes is more stable. [1]
(i)
Sketch a graph showing the variation with the mass number of the binding energy per nucleon. Mark with a cross (x) a point on your graph which
15
represents the most stable nuclide. (ii)
[3]
Hence explain why fusion of nuclei having high nucleon numbers is not associated with a release of energy.
TJC P3 4
(a)
A bar magnet is suspended from the free end of a helical spring as shown in Fig. 4.1. A pole of the magnet is situated near to one end of the solenoid.
Fig. 4.1 State and explain the motion of the magnet (i) (ii) (b)
when a direct current in the solenoid is switched on, and
[2]
when an alternating current passes through the solenoid.
[3]
In Fig. 4.2, a 10 MW nuclear power station produces electrical voltage at 600 V. It uses a step-up transformer with a turns ratio of 1: 200 to increase the voltage before transmitting it over long-distance cables of total resistance 15 Ω.
16
Fig. 4.2 Calculate the power lost as heat in the cables. 1.04 x 105 W 6
(a)
(b)
(i)
Explain what is meant by the term internal energy of a gas.
(ii)
What additional fact may be stated about the internal energy of a gas if the gas is ideal? [1]
[1]
1.0 mole of helium gas, assumed to behave ideally, is contained within a metal cylinder which is not insulated. The cylinder has a frictionless piston, as shown in Fig. 6.1. 1 mole of helium gas piston
Fig. 6.1 Heat is supplied to the gas and its temperature changes from 20 °C to 120 °C. (i)
Show that the change in the internal energy of the gas 1250 J.
[2]
Calculate the increase in volume of the helium gas as a result of the rise in temperature from 20 ºC to 120 ºC if the gas is maintained at the atmospheric pressure of 1.01 x 105 Pa. [2] 8.23 x 10-3 m3 (iii) Calculate the heat that has to be supplied to the gas in the cylinder for the expansion described in (ii) to occur. [3] 2080 J
(ii)
(c)
The helium gas in (b) is then compressed back to its initial volume by applying an external force on the piston. The process is carefully controlled so that the temperature of the helium gas remains constant at 120 °C. (i)
Calculate the final pressure of the gas.
1.36 x 105 Pa
[3]
17
(ii)
(d)
State whether heat energy will be absorbed or given out by the gas in the process described in (c)(i). Explain your answer. [3]
An electric kettle, rated 240 V 5.0 A, contains some water. The kettle is switched on and the temperature of water is found to rise at the rate of 9.0 °C per minute. The specific heat capacity of water is 4.2 × 103 J kg-1 K-1. (i) Calculate the mass of water in the kettle. 1.9 kg
7
(a)
(b)
[3]
(ii)
State and explain whether your answer to (d)(i) is greater or smaller than the actual mass of the water contained in the kettle.
(i)
Explain the meaning of the term diffraction.
(ii)
How does the width of the aperture through which a wave is passing affect the diffraction of the wave? [1]
[1]
A progressive sound wave of wavelength λ is incident on an open pipe as shown in Fig. 7.1. The length of the pipe is λ. A stationary wave is formed in the pipe.
λ direction of incident wave
Fig. 7.1
(c)
(i)
Describe the formation of the stationary wave in the pipe.
(ii)
On Fig. 7.1, sketch the shape of the stationary wave in the pipe. Mark the positions of the nodes and antinodes with the letters N and A respectively.
[2]
[2]
(i)
Electromagnetic waves have a wave nature as well as a particulate nature. Briefly describe a situation in which particles can be shown to have a wave nature. [1]
(ii)
Calculate the wavelength of a particle of mass 1.82 × 10-28 kg and kinetic energy 8.2 × 10-14 J. [3] 1.21 x 10-13 m
18
(iii) If the position of the particle can be determined to within the wavelength you have calculated in part (ii), determine the uncertainty in the particle’s momentum. 4.36 x 10-22 Ns [2] (d)
Fig. 7.2 represents part of the emission spectrum of atomic hydrogen. It contains a series of lines in the ultraviolet region, two wavelengths of which are marked. There are no lines in this series with wavelengths less than 91.2 nm.
91.2 (i)
121.6
λ /nm
Fig. 7.2 Calculate the photon energies corresponding to the wavelengths marked.
1. 91.2 nm 2.18 x 10-18 J 2. 121.6 nm 1.64 x 10-18 J [3] (ii)
With the aid of an energy level diagram, explain why the lines in the series get closer for smaller wavelengths. [2]
(iii) Explain why it is that although there are an infinite number of lines in this spectrum, the spectrum is nevertheless seen as a line spectrum. [3] (iv) Electrons emitted by a hot filament pass through a tube containing hydrogen gas and are then collected by an anode which is maintained at a positive potential with respect to the filament. The gas is found to emit monochromatic ultraviolet radiation. Suggest a reason why the radiation is monochromatic. [1]
19
VJC P2 4. The setup in Fig. 4.1 shows the top view of a 12 V DC supply connected in series with a rod PQ of length 0.50 m. The rod has a resistance of 24 Ω. The frictionless connecting rails are very long and have negligible electrical resistance. The rod lies in a region of a uniform magnetic field. The magnetic field strength is 1.0 T and the direction of the field is perpendicular to and acts into the plane of the page. The two ends of the rod rest on the rails and are free to move in the plane of the rails. The rod is initially at rest.
P
Z Conducting rail magnetic field acts vertically downwards
12 V switch
rod
Fig. 4.1
Conducting rail Y
Q
Fig. 4.2 shows the side view of the setup. The conducting rails are inclined at an angle of 30o above the horizontal.
I
rod
Q
I
Conducting rail Y
B = 1.0 T
30o Fig. 4.2
The mass of the rod is 20 g. (a) On Fig. 4.2, draw the forces acting on the rod.
[1]
(b) Calculate the initial acceleration of the rod when the switch is closed, and state its direction. [3] -2 5.9 ms up the slope (c) Calculate the circuit current when the rod reaches terminal velocity.
[2]
0.23 A (d) The moving rod PQ functions like a source of e.m.f. Identify the end of the rod (P or Q) which is at the higher potential. Explain your answer. [2]
20
5. Two blocks of copper are maintained at the same positive electrical potential of +4.00 V. If they are brought close together, until their separation is 5.00 × 10-10 m, then there is a finite probability that an electron from either block will tunnel across the gap between them and appear on the other side. (a) Calculate the electrical potential energy of an electron in either of the two blocks, expressing your answer in electron-volts. Take the potential energy of the electron at an infinite distance away from the blocks to be zero. [2] - 4.0 eV (b) Draw a diagram to show how the electrical potential energy of an electron varies as it moves from a point inside one block across the gap to a point inside the other block. Take the potential energy of the electron in the gap to be zero. [1]
The transmission coefficient T for an electron to tunnel across a potential barrier of width d is given by T ∝ exp(−2kd), where k =
2m(V0 − E ) , with m being the η
mass of the electron, V0 being the height of the barrier and E being the total energy of the electron. (c) When electrons of energy 1.0 eV approach the gap from within the block, the probability of successful tunnelling is T. If the width d of the gap is increased by 10 %, determine the new value of the energy E of the electrons such that the probability of successful tunnelling remains at the same value T. [3] 1.52 eV
(d) A stream of electrons of the same energy hits the above barrier at a rate equivalent to a current of 4.00 µA. If it is known that the probability of successful tunnelling is 1.83 × 10-12, determine the rate of tunnelling of electrons through the barrier. [2] -1 45.8 s
21
4. In a photoelectric emission experiment, a metal surface in an evacuated tube was illuminated with light. The graph below shows the stopping potential as a function of the frequency of the incident light falling on the metal surface.
(a) Deduce a value of Planck’s constant from Fig. 8.1. 6.6 x 10-34 Js
[3]
(b) Determine the work function for this metal, expressing it in electron-volts. [2] 5.4 eV (c) Explain the observation that the graph in Fig. 8.1 does not extend below the horizontal axis. [1] (d) The work function of a metal in air increases over time. Suggest a reason why. [2] 5. (a) In a ruby laser, a xenon discharge lamp surrounding a ruby crystal supplies light energy to the chromium atoms inside the ruby crystal in a process called optical pumping. Fig. 5.1 shows the energy levels of chromium atoms embedded in the ruby crystal.
electron energy / 2.20
E2
1.79
E1 Fig. 5.1
0
E0 (ground state)
22
(i) With reference to Fig. 5.1, deduce the wavelength of the light from the xenon lamp that is absorbed by the chromium atoms during optical pumping. [2] 565 nm (ii) Calculate the wavelength of the laser light emitted by the chromium atoms. [1] 694 nm (iii) Explain why the power supplied by the xenon lamp via optical pumping must exceed a certain minimum value before the ruby laser produces laser light of usable power. [2] (b)
Scientists are trying to fuse isotopes of hydrogen together with the use of lasers, in an effort to produce clean renewable energy. In such experiments, many laser beams are focussed onto a tiny pellet of fuel containing 1.00 × 10-4 kg of deuterium (an isotope of hydrogen with one proton and one neutron). In order for the deuterium nuclei to fuse and produce nuclear energy, the temperature of the fuel pellet must be raised to around 1.00 × 108 K in a short time of about 1.00 × 10-12 s. Determine the power of the laser system needed for such nuclear fusion to occur. (Hint: You may assume that the deuterium behaves like an ideal gas after it is vaporised by the laser beams.) [3] 6.19 x 1019 W 7.(a) (i) Explain what is meant by internal energy of a system. State what constitutes the internal energy of an ideal gas. [2] (ii) State two factors which determine the internal energy of an ideal gas.
[2]
(iii) An ideal gas is kept in a sealed container in a car which suddenly increases in speed. Discuss whether the internal energy of the gas will increase. [2] (b) Evaporation of sweat is an important mechanism for temperature control in humans. (i) Using a simple kinetic model for matter, explain how evaporation of sweat can help in temperature control in humans. [2] (ii) A 60.0 kg runner expends 300 W of power while running a marathon. Assuming that 10 % of the energy is delivered to muscle tissues and that the excess energy is primarily removed from the body by sweating, determine the volume of bodily fluid (assume it is water) lost per hour. Take the specific latent heat of water to be 2.41 × 106 J kg-1. [3] 4.03 x 10-4 m3 h-1 (iii) Suggest, with a reason, whether the runner loses the amount of sweat calculated in (ii) in a practical situation. [2] (c) A scuba diver descends to 8.2 m below the surface of the sea. (i) Estimate the pressure (in atmospheres) that her scuba-diving tank regulator would need to supply so that her lungs can fill as normal. [2] 1.8 atm
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(ii) Calculate the ratio of the number of air molecules in her lungs at a depth of 8.2 m to the number of molecules in her lungs at the surface. [2] 1.8 (iii) State an assumption made in the calculations in (ii)
[1]
(iv) If the diver ascends too quickly, bubbles will form in his blood, a painful and potentially dangerous situation known as the “bends”. Suggest how this could come about. [2] 8. (a) Describe how two samples, one emitting alpha particles, and the other emitting beta particles can be distinguished through a simple school laboratory experiment, using a Geiger-Muller (GM) tube connected to a ratemeter. [3] (b) Radon (Rn) decays spontaneously with a half-life of 52 s to form polonium (Po) and polonium in turn decays spontaneously with a half-life of 0.16 s to form lead (Pb). 220 86
X
216 84
Rn
52 s
212 82
Po
Pb
0.16 s
(i) Define the terms activity and decay constant.
[2]
(ii) State the identity of the particle labelled X and write down the first decay equation in the series in (b). [2] (iii) Suppose the activity of radon, Rn, is determined by measuring the number of particles X emitted. Explain how the decay of 216 84 Po will affect the measurement. [3] (c) Radioactive isotopes are often introduced into the body through the bloodstream. Their spread through the body can then be monitored by detecting the appearance of radiation in different organs. Iodine-131 (131I), a beta emitter with a half-life of 8.04 days, is one such tracer. Suppose a scientist introduces a sample of 131I with an activity of 375 Bq into the body and watches it spread to the organs. (i) Discuss the difference between a photoelectron and a beta-particle by making reference to their origin. [2] (ii) Assuming that all of the 131I atoms in the sample went to the thyroid gland, calculate the decay rate in the thyroid 2.5 weeks later. Assume that none of the 131 I is eliminated by the body through physiological means. [3] 82.9 Bq (iii) Calculate the mass of 8.2 x 1017 kg
131
I required to produce an activity of 375 Bq.
[3]
(d) State one similarity and one difference between radioactive decay and nuclear fission. [2]
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