Name: Date:. Isotopes provide evidence for the existence of A. protons. B. electrons. C. nuclei. Topic 7 &3 Review Atomic, Nuclear, and Quantum Physics D. neutrons.. The atomic line spectra of elements provides evidence for the existence of A. photons. B. electrons. C. quantized energy states within nuclei. D. quantized energy states within atoms. 3. The number of nucleons in a nucleus is the number of A. particles in the nucleus. B. neutrons in the nucleus. C. protons in the nucleus. D. protons plus neutrons in the nucleus. 4. The nucleus of an atom contains protons. The protons are prevented from flying apart by A. the presence of orbiting electrons. B. the presence of gravitational forces. C. the presence of strong attractive nuclear forces. D. the absence of Coulomb repulsive forces at nuclear distances.
5. The diagram below shows the path followed by an alpha-particle in the vicinity of the nucleus of a gold atom. alpha-particle nucleus Which of the following is correct for the alpha-particle? A. The force acting on it changes direction. B. The force acting on it is smaller than that acting on the nucleus. C. Its potential energy is constant. D. Its kinetic energy is constant. 6. Which of the following identifies the significant interaction(s) between nucleons inside the nucleus? A. Nuclear only B. Coulomb only C. Nuclear and Coulomb D. Gravitational, nuclear and Coulomb 7. The Bohr model of the hydrogen atom predicts A. the line spectra of multi-electron atoms. B. the wavelengths of the principal lines in the spectrum of atomic hydrogen. C. the wavelengths in the spectrum of molecular hydrogen. D. the relative intensities of the spectral lines of atomic hydrogen.
8. The diagram below shows four energy levels in an atom, together with some possible electron transitions. E 4 E 3 E E Which one of the following best represents the emission line spectrum produced from these transitions? A. increasing wavelength B. C. D. 9. The following are statements concerning radioactive decay. I. Alpha particles have discrete energies. II. III. The beta-energy spectrum is a broad continuous distribution of energies. Gamma rays are emitted with discrete energies. Which statement(s) is(are) evidence for the existence of nuclear energy levels? A. I only B. II only C. III only D. I and III only 3
. The diagram below shows three energy levels of a certain atom. 5. ev T S 5. ev The photon associated with the energy change T has frequency f T and the photon associated with the energy change S has frequency f S The ratio f f S T is A.. 3 B.. C.. D. 3.. The spectrum of energy of β -particles emitted in radioactive decay is explained on the basis of A. the emission of neutrinos during the decay process. B. the emission of antineutrinos during the decay process. C. the absorption of neutrinos during the decay process. D. the absorption of antineutrinos during the decay process.. Radioactive element P has a half-life of 3 days and element Q has a half-life of days. Initially a radioactive source contains equal numbers of each element. What is the ratio number of atoms of number of atoms of P Q after 6 days have elapsed? A. B. C. 3 3 D. 4
3. An isotope of radium has a half-life of 4 days. A freshly prepared sample of this isotope contains N 7N atoms. The time taken for 8 of the atoms of this isotope to decay is A. 3 days. B. 6 days. C. days. D. 8 days. 4. The decay constant λ of a nuclide with a long half-life may be determined using the equation activity = λ number of nuclei present. Which of the following is the best explanation as to why this equation may be used? A. The decay constant λ is very large. B. The number of nuclei in a sample decreases rapidly. C. The activity of the sample decreases slowly. D. The sample contains a large number of nuclei. 5. The decay constant λ in radioactive decay is defined as A. the probability of decay per unit time of a nucleus. B. the probability of decay of a nucleus. C. the constant ln T where T is the half-life. D. the constant in the radioactive decay equation N = N e λt. 6. Radioactive decay is a random process. This means that A. a radioactive sample will decay continuously. B. some nuclei will decay faster than others. C. it cannot be predicted how much energy will be released. D. it cannot be predicted when a particular nucleus will decay. 5
7. A nucleus of uranium-33 ( 33 U) 9 undergoes α- decay. Which of the following correctly identifies the number of protons Z and the number of neutrons N of the nucleus produced by this decay? Z N A. 9 9 B. 9 39 C. 88 3 D. 88 4 8. The activity of a sample of Iodine-3 is plotted as a function of time as shown below. The activity scale is logarithmic. 9 8 7 6 5 4 3 Activity / Bq 9 8 7 6 5 4 3 3 4 5 6 time / days The half-life of Iodine-3 is close to A. 8 days. B. 55 days. C. 8 days. D. 8 days. 6
9. In a laboratory when aluminium nuclei are bombarded with α-particles, the following reaction may take place. 4 7 3 He + 3Al 5P + n This reaction is an example of A. nuclear fission. B. nuclear fusion. C. natural radioactive decay. D. artificial transmutation.. An electron of mass m e and a proton of mass m p are moving with the same speed. The de Broglie wavelengths associated with the electron and with the proton are λ e and λ p respectively. The ratio λ p λe is equal to mp A.. m e me B.. m p mp C.. m e me D.. m p. A beam of electrons of uniquely defined wavelength λ is incident on an aperture of height d. The beam is traveling along the x direction. The height d is of the same order as λ. After passing through the aperture, the component of momentum in the x direction is p x and the component in z the direction is p z. Which of the following shows the uncertainty in p x and the uncertainty in p z? 7
p x p z A. B. C. D. h 4πd h πd h 4πd h 4 4πd. Which of the following correctly describes the nature of the energy spectra of alpha (α), beta (β) and gamma (γ) radiation? α β γ A. discrete continuous discrete B. continuous discrete discrete C. discrete discrete continuous D. continuous continuous discrete 3. Which of the following phenomena provides evidence for de Broglie s hypothesis? A. Electron diffraction B. X-ray production C. Line spectra D. Nuclear energy levels 4. Which of the following is the correct relationship between the kinetic energy E k of a particle and its associated de Broglie wavelength λ? A. λ E k B. λ C. λ D. λ E E k k E k 8
5. A particle has kinetic energy E and its associated de Broglie wavelength is λ. The energy E is proportional to A. λ. B. λ. C. λ. D. λ. 6. Which one of the following best shows the variation with kinetic energy E of the de Broglie wavelength λ associated with a particle? A. B. E E C. D. E E 7. When electrons of suitable energy travel through a thin layer of graphite, a pattern of concentric circles is produced on a screen. fine beam of electrons graphite fluorescent screen The production of this pattern is evidence for A. the wave nature of the electron. B. the nuclear model of the atom. C. the particle nature of the electron. D. the existence of X-rays. 9
8. Monochromatic light is incident on a metal surface in a photocell. Which of the following statements is correct? A. The rate at which electrons are emitted from the surface is proportional to the intensity of the radiation. B. The rate at which electrons are emitted from the surface depends only on the frequency of the radiation used. C. The intensity of the radiation used must be greater than a threshold value in order to emit electrons. D. The wavelength of the radiation must be greater than a threshold value in order to emit electrons. 9. The graph shows the variation with frequency f of the maximum kinetic energy E k of photoelectrons emitted from a metal surface S. E k f Which one of the following graphs shows the corresponding variation for a metal surface with a higher work function? The dotted line on each graph shows the variation for metal S. A. E k B. E k f f C. E k D. E k f f
3. When light is incident on a metal surface, electrons may be ejected. The following graph shows the variation with frequency f of the maximum kinetic energy E k max of the ejected electrons. E max k f Which one of the following graphs best shows the variation with frequency f of the maximum kinetic energy E k max of the ejected electrons if another metal surface with a lower threshold frequency is used? A. E max k B. E max k f f C. E max k D. E max k f f 3. In an experiment to investigate the photoelectric effect, monochromatic light is incident on a metal surface. The photoelectric current and the maximum kinetic energy of the photoelectrons are measured. Which one of the following correctly shows the change, if any, in the photoelectric current and in the maximum kinetic energy of the photoelectrons when light of the same intensity but higher frequency is incident on the same metal surface? Photoelectric current Maximum kinetic energy A. decreases no change B. decreases increases C. no change decreases D. no change increases
3. In an experiment to demonstrate the photoelectric effect, light of intensity L and frequency f is incident on a metal surface. The maximum photoelectric current is I and the stopping potential is V S. What change if any occurs in the maximum photoelectric current and in the stopping potential when light of the same intensity L but of frequency f is incident on the surface? maximum photoelectric current stopping potential A. I greater than V S B. less than I greater than V S C. I less than V S D. less than I less than V S 9 33. A nucleus 38 Sr decays by the emission of an electron. What are the mass (nucleon) number and the atomic (proton) number of the resulting nucleus? Mass number Proton number A. 89 38 B. 9 39 C. 9 38 D. 9 39 34. Which one of the following diagrams best illustrates the first two stages of an uncontrolled fission chain reaction? A. Key : neutron uranium nucleus fission fragment B. C. D.
35. A student suggests that the following transformation may take place. Measurement of rest masses shows that 4 4 4 7 7 N+ He 8 O+ total rest mass( N 4 7 + He ) < total rest mass( O 8 + p ) The student concludes that the reaction will A. take place if the helium nucleus has sufficient kinetic energy. B. always take place and the proton will be emitted with kinetic energy. C. always take place but the proton will have zero kinetic energy. p 7 D. never take place because there is no mass defect. 7 36. The binding energy per nucleon of the nucleus 3 Li is approximately 5 MeV. The total energy required to completely separate the nucleons of this nucleus is approximately A. 5 MeV. B. MeV. C. 35 MeV. D. 5 MeV. 37. The graph below shows the variation with mass (nucleon) number of the average binding energy per nucleon. mass number average binding energy per nucleon II I IV III Which direction indicates a fission reaction with a release of energy? A. I B. II C. III D. IV 3
64 38. A freshly-prepared sample of cobalt-64 ( Co ) decays by the emission of γ-ray photons. The decay may 7 be represented by the nuclear equation After this decay, the binding energy per nucleon has 64 64 7 Co 7Co + energy. A. increased in magnitude because energy has been emitted from the nucleus. B. decreased in magnitude because energy has been emitted from the nucleus. C. stayed constant because the number of nucleons in the nucleus is unchanged. D. stayed constant because the proton number is unchanged. 39. Either of the two following graphs is useful in predicting nuclear energy changes in fission and fusion processes. Y Y X X Which one of the following correctly identifies the quantities X and Y? X Y A. atomic number total binding energy B. mass number total binding energy C. atomic number average binding energy per nucleon D. mass number average binding energy per nucleon 4
4. The diagram below shows the deflection chamber of a mass spectrometer. source of ions A B X C region of uniform magnetic field D Track X shows the path of a singly-charged carbon- ion in the chamber. Which track best shows the track of a singly-charged C-4 ion that has the same initial speed? A. A B. B C. C D. D 4. This question is about atomic spectra. An electron undergoes a transition from an atomic energy level of 3. 5 J to an energy level of.3 5 J. Determine the wavelength of the emitted photon................ (Total 3 marks) 4. This question is about a proton. The proton particle is made out of three quarks. (a) Explain why the three quarks in the proton do not violate the Pauli exclusion principle.... 5
(b) Quarks have spin. Explain how it is possible for the proton to also have spin....... (Total 4 marks) 43. This question is about calculating the distance of closest approach of an α-particle to a nucleus. An α-particle approaches a nucleus of palladium. The initial kinetic energy of the α-particle is 3.8 MeV. The particle is brought to rest at point P, a distance d from the centre of the palladium nucleus. It then moves back along the path from which it came as shown in the diagram below. palladium nucleus -particle P d (a) Calculate the value, in joules, of the electric potential energy of the α-particle at point P. Explain your working.......... (b) The atomic (proton) number of palladium is 46. Calculate the distance d................ (c) Gold has an atomic (proton) number of 79. Explain whether the distance of closest approach of this α-particle to a gold nucleus would be greater or smaller than your answer in (b)....... 6
(d) The radius R of a nucleus of mass (nucleon) number A is given by 5 A R =. 3 m. (i) State in terms of the unified atomic mass unit u, the approximate mass of a nucleus of mass number A. (ii) 4πR The volume of a sphere of radius R is given by V = 3. Deduce that the density of all nuclei is approximately 7 kg m 3. 3 (Total 8 marks) 44. This question is about the wave nature of matter. (a) Explain what is meant by the de Broglie wavelength of a particle.......... (b) Calculate the de Broglie wavelength of an electron that has been accelerated from rest through a potential difference of 5. kv................ (4) (Total 6 marks) 7
45. Light of wavelength 6. 7 m is incident normally on a plane surface as shown below. Incident light, wavelength 6. 7 m Surface The light photons are absorbed by the surface. (a) Show that, for one photon of the light, (i) its energy is 3.3 9 J; (ii) its momentum is. 7 kg m s. (b) The light has intensity 5. W m. Determine, for an area of. m of the plane surface, (i) the number of photons incident per second. (ii) the change in momentum per second of the photons. 8
(c) (i) Using your answers in (b), state the pressure exerted by the light on the surface. (ii) State and explain what would happen to this pressure if the light is reflected rather than absorbed by the surface. (Total marks) 46. This question is about models of the hydrogen atom. In 93 Niels Bohr developed a model of the hydrogen atom which successfully explained many aspects of the spectrum of atomic hydrogen. (a) State one aspect of the spectrum of atomic hydrogen that Bohr s model did not explain....... Bohr proposed that the electron could have only certain stable orbits. These orbits are specified by the relation mvr = nh with n =,, 3... π where m is the mass of the electron, v its speed, r the radius of the orbit and h the Planck constant. This is sometimes known as Bohr s first postulate. (b) State the other postulate proposed by Bohr............. By using Newton s second law and the Coulomb law in combination with the first postulate, it can be shown that r = n h 4π mke where k = 4πε. 9
It can also be shown that the total energy E n of the electron in a stable orbit is given by ke E n = r. (c) Using these two expressions, deduce that the total energy E n may be given as K E n = n where K is a constant............. (d) State and explain what physical quantity is represented by the constant K.......... (e) Outline how the Schrödinger model of the hydrogen atom leads to the concept of energy levels............. (Total marks)
47. This question is about atomic models. The Bohr model was developed in order to explain the atomic spectrum of hydrogen. (a) Explain how the Bohr model was used to explain the spectrum of atomic hydrogen................... (4) (b) State one limitation of the Bohr model............. A later model of the atom was developed by Schrödinger. (c) (i) State two differences between the model of Bohr and the model of Schrödinger. (ii) Explain how the Schrödinger theory is consistent with the Heisenberg uncertainty principle. (Total marks)
48. This question is about the photoelectric effect. The apparatus shown below may be used to investigate the photoelectric effect. monochromatic incident light window metal plate vacuum electrode A V The potential difference V applied between the metal plate and electrode may be varied in magnitude and in direction. This is repeated for different values of intensity for the same frequency of light. (a) Monochromatic light is incident on the metal plate. The potential difference between the plate and the electrode is adjusted so that the reading on the microammeter is a maximum. The graph below shows the variation with intensity of the monochromatic light of the maximum current. maximum current intensity Explain the features of this graph................... (4)
(b) The frequency and the intensity of the light are held constant. The graph below shows the variation with the potential difference V of the current I measured on the microammeter. I V V The frequency of the light is doubled at a constant intensity. On the graph above, draw a second line to show the variation with potential difference of the current in the microammeter. (Total 7 marks) 49. Photoelectric effect A metal is placed in a vacuum and light of frequency f is incident on its surface. As a result, electrons are emitted from the surface. The graph below shows the variation with frequency f of the maximum kinetic energy E K of the emitted electrons. (a) The graph above shows that there is a threshold frequency of the incident light below which no electrons are emitted from the surface. With reference to the Planck constant and the photoelectric work function, explain how Einstein s photoelectric theory accounts for this threshold frequency................... (4) 3
(b) Use the graph in (a) to calculate the (i) threshold frequency. (ii) Planck constant. (4) (iii) work function of the metal. (Total marks) 5. This question is about photoelectric effect. In the photoelectric effect, electrons are emitted from a metal surface when light of a suitable frequency is incident on the surface. The diagram below shows an arrangement for investigating some aspects of the photoelectric effect. light P evacuated quartz tube Q µa µa variable dc supply P and Q are metal plates. Monochromatic light of frequency f is incident on plate P. In the situation shown, the microammeter (µa) registers a current. The intensity of the light is kept constant throughout the experiment. 4
(a) As the potential difference between P and Q is increased, the current in the circuit decreases until it is zero. State and explain the polarity of the metal plate Q................... (4) (b) The potential difference in the circuit is increased until the current in the circuit just becomes zero. The potential difference is then kept constant. The frequency f of the light is increased to a new value and the intensity is kept constant. The microammeter again registers a current. Outline how Einstein s theory of the photoelectric effect accounts for this observation................ (c) Explain why in (b) as f is increased at constant intensity, the current registered by the microammeter decreases.......... (d) At a frequency f of 3. 5 Hz, the potential difference between P and Q at which the current just becomes zero is 8. V. The work function of the metal surface of P is 4.4 ev. Determine a value for the Planck constant................ (Total marks) 5
5. Emission of electrons The diagram below shows an electron on the surface of a metal. Electromagnetic radiation is incident normally on the surface. incident electromagnetic radiation metal surface 5. m electron area from which electron can absorb energy According to a model based on the electromagnetic theory of light, the electron absorbs all the energy that is incident on the surface within a distance of 5. m from the electron. The intensity of light incident on the surface is.6 W m. The energy required to remove an electron from the surface is.8 ev. (a) Calculate, on the basis of this model, that the time taken for the electron to gain sufficient energy to leave the surface is 3 s. (The area of a circle of radius R is πr.)............... (4) (b) Experimental observation indicates that electrons are emitted from the surface in less than 9 s. Explain how this observation is consistent with the particle theory of light............. 6
(c) The diagram below illustrates an apparatus used to investigate the photoelectric effect. light evacuated tube metal plate collecting plate A variable voltage V (i) Describe how, using this apparatus, the maximum kinetic energy of the emitted electrons may be determined for incident light of frequency f. (ii) On the axes provided below draw a sketch graph to show the variation with frequency f of the maximum kinetic energy E K of the emitted electrons. (Numerical values are not required.) E K f (iii) State and explain what is represented by the gradient (slope) of the graph. 7
(d) The incident light has intensity.6 W m, wavelength 5 nm and 5.% of the incident photons cause the ejection of electrons from the surface. Determine the number of electrons ejected from. m of the surface per second............. (Total 5 marks) 5. This question is about the photoelectric effect. (a) State three pieces of evidence provided by the photoelectric effect that support the particle nature of electromagnetic radiation............... 3....... The graph below shows the variation with frequency f of the stopping potential V S for photoelectrons emitted from a metal surface. V s / V..5..5..9....3.4.5 5 f / Hz 8
The photoelectric equation may be written in the form of the word equation photon energy = work function + maximum kinetic energy of electron. (b) (i) State this equation in terms of f and V S, explaining all other symbols you use. (ii) Use your equation to deduce that the gradient of the graph is e h. (iii) Given that the Planck constant is 6.6 34 J s, calculate a value for the work function of the surface. (Total marks) 53. This question is about nuclear reactions. (a) Complete the table below, by placing a tick ( ) in the relevant columns, to show how an increase in each of the following properties affects the rate of decay of a sample of radioactive material. Property temperature of sample pressure on sample amount of sample Effect on rate of decay increase decrease stays the same Radium-6 ( 6 88 Ra) undergoes natural radioactive decay to disintegrate spontaneously with the emission of an alpha particle (α-particle) to form radon (Rn). The decay constant for this reaction is 4.3 4 yr. The masses of the particles involved in the reaction are radium: radon: α-particle: 6.54 u.76 u 4.6 u 9
(b) (i) Explain what is meant by the statement that the decay constant is 4.3 4 yr. (ii) Calculate the energy released in the reaction. (c) The radium nucleus was stationary before the reaction. (i) Explain, in terms of the momentum of the particles, why the radon nucleus and the α-particle move off in opposite directions after the reaction. (ii) The speed of the radon nucleus after the reaction is v R and that of the α-particle is v α. Determine the ratio v α. v R A college has been using a sample of radium-6 as an α-particle source for 3 years. Initially, the mass of radium was 5. µg. (d) Determine (i) the initial number of atoms of radium-6 in the sample; 3
(ii) the number of atoms of radium-6 in the sample after 3 years; (iii) the average activity of the sample during the 3 year period. (6) (e) The α-particle is composed of protons and neutrons. Describe, by reference to the structure of the proton and the neutron, why they are not classed as fundamental particles............. Another type of nuclear reaction is a fusion reaction. This reaction is the main source of the Sun s radiant energy. (f) (i) State what is meant by a fusion reaction. (ii) Explain why the temperature and pressure of the gases in the Sun s core must both be very high for it to produce its radiant energy. High temperature:...... 3
...... High pressure:............ (5) (Total 3 marks) 54. This question is about models of the hydrogen atom. (a) The Bohr model provides a partially successful explanation of the spectrum of the hydrogen atom. The model predicts that the energy, E, of the electron in the hydrogen atom is given by E =.8 n 8 where n is an integer and E is in joules. (i) By reference to this equation, describe how the Bohr model accounts for the line spectrum of the hydrogen atom. (4) (ii) Calculate the shortest wavelength of light in the spectrum of atomic hydrogen. (iii) State one characteristic of the spectrum of atomic hydrogen which cannot be accounted for by the Bohr model. 3
(b) Outline by reference to position and momentum how the Schrödinger model of the hydrogen atom is consistent with the Heisenberg uncertainty principle.......... (Total marks) 55. This question is about the nuclear structure of the atom and atomic energy levels. When the electron was first discovered it led to the idea that an atom consists of a lump of positive charge in which the electrons are embedded. In 9 Geiger and Marsden carried out an experiment to test the validity of this idea. The results of their experiment in fact suggested that the atom is mostly empty space with an electrically charged nucleus of relatively large mass occupying only a small amount of space. (This is the so-called nuclear model of the atom). Their experiment involved firing alpha particles at a thin sheet of gold foil. (a) State the nature of an alpha particle.... The diagram below shows a small part of the gold foil with two alpha particles A and B approaching the foil. A B gold foil 33
(b) (i) Some alpha particle trajectories lead to the idea that most of the atom is empty space. On the diagram, draw such a trajectory for the alpha particle A. (ii) Some other alpha particle trajectories lead to the idea that the atom has an electrically charged, relatively massive nucleus. On the diagram, draw such a trajectory for the alpha particle B. (iii) Describe briefly how these trajectories lead to the idea of the nuclear model of the atom. (4) In 94 Niels Bohr suggested that the electrons in an hydrogen atom occupy discrete energy levels. The diagram below shows some of the principal energy levels. n = 8 n = 3 energy n = n = (c) (i) Label with the letter X, the energy level in which an electron will have zero potential energy. (ii) Explain how the line spectra of atomic hydrogen supports the idea of discrete energy levels. You may use the diagram above to support your answer. 34
(4) (Total marks) 56. This question is about nuclear energy and radioactive decay. (a) A neutron collides with a nucleus of uranium-35 and the following reaction takes place. 35 96 38 9 U + n 37Rd + 55Cs + Using the data below, calculate the energy, in MeV, that is released in the reaction. n mass of mass of 35 9 U = 35.439 u 96 37 Rb = 95.934 u mass of 38 55 Cs = 37.9 u mass of n =.87 u............ (4) (b) The reaction in (a) is more likely to take place if the colliding neutron has an energy of about. ev. In certain types of nuclear reactors in which this reaction might take place, the neutrons produced have their energy reduced by collisions with nuclei of graphite ( C). The law of conservation of momentum can be used to estimate the number of collisions required to reduce the energy of the neutrons to. e V. State the law of conservation of momentum.......... (c) A neutron has a kinetic energy of. MeV. Deduce that the speed of the neutron is.95 7 m s.......... 35
(d) You may assume that the mass of a nucleus of graphite is twelve times the mass of a neutron. In a certain collision between a neutron and a stationary graphite nucleus, the neutron of kinetic energy. MeV, rebounds from the graphite nucleus in a direction along a line joining the centres of the nucleus and neutron. 7.95 m s 7.65 m s v =.3 7 m s neutron graphite before collision after collision The rebound speed of the neutron is.65 7 m s. (i) Deduce that the speed v of the graphite nucleus after collision is.3 7 m s. (ii) Using your answer in (i), deduce whether the collision is elastic or inelastic. (iii) Use your answer to (ii) to deduce that each time a neutron collides in this manner with a graphite nucleus it loses about 3% of its kinetic energy. (iv) Explain briefly, why quite a lot of collisions are necessary to reduce the energy of the neutron to. ev. 36
(e) Determine the de Broglie wavelength associated with a neutron that has a kinetic energy of. MeV............. (4) 38 (f) The nucleus of 55 Cs produced in the fission reaction 96 38 9 U + n 37Rd + 55Cs + 35 is radioactive. It undergoes β decay to a nucleus of barium (Ba). 38 (i) Write down the equation for the decay of 55 Cs. n (ii) State the name of the force and the name of exchange particle involved in β decay. Force:... Exchange particle:... (g) The graph below shows the variation with time t of the percentage of nuclei of caesium-38 and the percentage of nuclei of the isotope of barium formed from the decay of a pure sample of caesium-38. 9 8 7 Cs % of nuclei 6 5 4 3 Ba 5 5 5 3 35 4 45 5 t / minutes 37
Use the graph, explaining your working, to estimate the half-life of (i) caesium-38. (ii) the isotope of barium. (Total 3 marks) 57. This question is about collisions and radioactive decay. (a) (i) Define linear momentum and impulse. Linear momentum:...... Impulse:...... (ii) State the law of conservation of momentum. (iii) Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium. 38
A stationary radon- ( 86 Rn ) nucleus undergoes α-decay to form a nucleus of polonium (Po). The α-particle has kinetic energy of 6.9 MeV. (b) (i) Complete the nuclear equation for this decay. 86 Rn Po + (ii) Calculate the kinetic energy, in joules, of the α-particle. (iii) Deduce that the speed of the α-particle is.74 7 m s. The diagram below shows the α-particle and the polonium nucleus immediately after the decay. The direction of the velocity of the α-particle is indicated. polonium nucleus -particle (c) (i) On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay. (ii) Determine the speed of the polonium nucleus immediately after the decay. (iii) In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i). 39
The half-life of the decay of radon- is 3.8 days and radon- has a half-life of 55 s. (d) (i) Suggest three ways in which nuclei of radon- differ from those of radon-............... 3....... (ii) Define half-life. (iii) State the expression that relates the activity A t at time t of a sample of a radioactive material to its initial activity A at time t = and to the decay constant λ. Use this expression to derive the relationship between the decay constant λ and the half-life T. (iv) Radon- emits α-particles. The activity of radon gas in a sample of. m 3 of air is 4.6 Bq. Given that. m 3 of the air contains.6 5 molecules, determine the ratio number of radon - atoms in. m number of moleculesin. m of air of air 3 3 (4) 4
(e) Suggest whether radon- or radon- presents the greater hazard to people over a long period of time....... (Total 3 marks) 58. This question is about radioactive decay. A nucleus of the isotope xenon, Xe-3, is produced when a nucleus of the radioactive isotope iodine I-3 decays. (a) Explain the term isotopes.......... (b) Fill in the boxes below in order to complete the nuclear reaction equation for this decay. 3 3 I Xe + + 54 The activity A of a freshly prepared sample of the iodine isotope is 6.4 5 Bq and its half-life is 8. days. (c) Using the axes, draw a graph to illustrate the decay of this sample. A / Bq 6.4 5 5. 5 5 time / days 4
(d) Determine the decay constant of the isotope I-3............ The sample is to be used to treat a growth in the thyroid of a patient. The isotope should not be used until its activity is equal to.5 5 Bq. (e) Calculate the time it takes for the activity of a freshly prepared sample to be reduced to an activity of.5 5 Bq............ (Total marks) 59. The Geiger-Nuttall theory of α-particle emission relates the half-life of the α-particle emitter to the energy E of the α-particle. One form of this relationship is L = 66 E 53.5. L is a number calculated from the half-life of the α-particle emitting nuclide and E is measured in MeV. Values of E and L for different nuclides are given below. (Uncertainties in the values are not shown.) Nuclide E / MeV L E / MeV 38 U 36 34 U U 4. 7.5.488 4.49 4.87.47 4.8.89.455 8 Th 5.4 7.78.. 8 Rn Po 6.4 3.6.44 7.39.75.368 (a) Complete the table above by calculating, using the value of E provided, the value of E for the nuclide 8 Th. Give your answer to three significant digits. 4
The graph below shows the variation with E of the quantity L. Error bars have not been added. L 6 8 4..3.4.5 / MeV E 4 8 (b) (i) Identify the data point for the nuclide Rn. Label this point R. 8 (ii) On the graph, mark the point for the nuclide Th. Label this point T. (iii) Draw the best-fit straight-line for all the data points. (c) (i) Determine the gradient of the line you have drawn in (b)(iii). 43
(ii) Without taking into consideration any uncertainty in the values for the gradient and for the intercept on the x-axis, suggest why the graph does not agree with the stated relationship for the Geiger-Nuttall theory. (d) On the graph above, draw the line that would be expected if the relationship for the Geiger-Nuttall theory were correct. No further calculation is required. (Total marks) 6. This question is about nuclear binding energy. (a) Define nuclear binding energy....... The axes below show values of nucleon number A (horizontal axis) and average binding energy per nucleon E (vertical axis). (Binding energy is taken to be a positive quantity). E / MeV 9 8 7 6 5 4 3 5 5 75 5 5 75 5 5 A (b) Mark on the E axis opposite, the approximate position of 56 (i) the isotope Fe (label this F). 6 44
(ii) the isotope H (label this H). 38 (iii) the isotope U (label this U). 9 (c) Using the grid opposite, draw a graph to show the variation with nucleon number A of the average binding energy per nucleon E. 3 (d) Use the following data to deduce that the binding energy per nucleon of the isotope He is. MeV. nuclear mass of mass of proton mass of neutron 3 He = 3.63 u =.78 u =.867 u............... In the nuclear reaction H + H 3 He + n energy is released. (e) (i) State the name of this type of reaction. (ii) Use your graph in (e) to explain why energy is released in this reaction. (Total marks) 45