UGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM BOOKLET CODE PH PHYSICAL SCIENCE TEST SERIES # 4 Atomic, Solid State & Nuclear + Particle SUBJECT CODE 05 Timing: 3: H M.M: 200 Instructions 1. This test paper has a total of 50 questions. All Questions are compulsory. 2. Each questions are 4 marks 3. Read the Questions carefully and mark your appropriate response to the OMR sheet. 4. There is Negative marking of 1/4 for each wrong answer. 5. Mark the response by Black or Blue Ball Pen only.. Calculator and mobile phone is not allowed during exam
1. A transition in which one photon is radiated by the electron in a hydrogen atom when the electron's wave function changes from ψ 1 to ψ 2 is forbidden if ψ 1 and ψ 2 A. have opposite parity B. are orthogonal to each other C. are zero at the center of the atomic nucleus D. are both spherically symmetrical 2. The wave function for identical fermions is antisymmetric under particle interchange. Which of the following is a consequence of this property? A. Pauli exclusion principle B. Bohr correspondence principle C. Heisenberg uncertainty principle D. Bose-Einstein condensation 3. Which of the following atoms has the lowest ionization potential? A. ²He₄ B. ⁷N 14 C. ⁵⁵Cs 133 D. ¹⁸Ar 40 4. A 3p electron is found in the 3 P 3/2 energy level of a hydrogen atom. Which of the following is true about the electron in this state? A. It is allowed to make an electric dipole transition to the 2 S 1/2 level B. It is allowed to make an electric dipole transition to the 2 P 1/2 level C. It has quantum numbers l = 3, j = 3/2, s = 1/2 D. It has quantum numbers n = 3, j = l, s = 3/2 5. The spacing of the rotational energy levels for the hydrogen molecule H₂ is most nearly A. 10 9 ev B. 10 3 ev C. 10 ev D. 10 MeV. The electronic energy levels of atoms of a certain gas are given by E n = E 1 n 2, where n = 1, 2, 3,... Assume that transitions are allowed between all levels. If one wanted to construct a laser from this gas by pumping the n = 1 n = 3 transitions, which energy level or levels would have to be metastable? A. n = 1 only B. n = 2 only C. n = 1 and n = 3 only D. n = 1, n = 2, and n = 3 7. One feature common to both the Debye theory and the Einstein theory of the specific heat of a crystal composed of N identical atoms is that the A. Average energy of each atom is 3kT B. Vibrational energy of the crystal is equivalent to the energy of 3Nindependent harmonic oscillators C. Crystal is assumed to be continuous for all elastic waves D. Speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves 8. The conventional unit cell of a body-centered cubic Bravais lattice is shown in the figure. The conventional cell has volume a 3. What is the volume of the primitive unit cell?
A. a 3 /8 B. a 3 /4 C. a 3 /2 D. a 3 9. The ratio of the energies of the K characteristic X-rays of carbon (Z = ) to those of magnesium (Z = 12) is most nearly A. ¼ B. ½ C. 1 D. 2 10. The Hall effect is used in solid-state Physics to measure A. ratio of charge to mass B. magnetic susceptibility C. the sign of the charge carriers D. the width of the gap between the conduction and valence bands 11. Consider a heavy nucleus with spin 1/2. The magnitude of the ratio of the intrinsic magnetic moment of this nucleus to that of an electron is A. Zero, because the nucleus has no intrinsic magnetic moment B. Greater than 1, because the nucleus contains many protons C. Greater than 1, because the nucleus is so much larger in diameter than the electron D. Less than 1, because the nucleus has a mass much larger than that of the electron 12. If a singly ionized Helium atom in an n = 4 state emits a photon of wavelength 470 nanometers, which of the following gives the approximate final energy level E f of the atom, and the n value, of n f this final state? E f (ev) n f A..0 3 B..0 2 C. 14 2 D. 14 1 13. Positronium is the bound state of an electron and a positron. Consider only the states of zero orbital angular momentum l = 0. The most probable decay product of any such state of positronium with spin zero (singlet is) A. 0 photons B. 1 photons C. 2 photons D. 3 photons 14. According to the Standard Model of elementary particles, which of the following is NOT a composite object? A. Muon B. Pi-meson C. Neutron D. Deuteron 15. The binding energy of a heavy nucleus is about 7 million electron volts per nucleon, whereas the binding energy of a medium-weight nucleus is about 8 million electron volts per nucleon. Therefore, the total kinetic energy liberated when a heavy nucleus undergoes symmetric fission is most nearly A. 187 MeV B. 938 MeV C. 200 MeV D. 8 MeV 1. Solid Argon is held together by which of the following bonding mechanism? A. Ionic bond only B. Covalent bond only C. Partly covalent and partly ionic bond D. Van der Waals bond
17. Given that the binding energy of the hydrogen atom ground state is E 0 = 13. ev, the binding energy of n = 2 state of positronium (positron-electron system) is A. 8E 0 B. 4E 0 C. E 0/ 2 D E 0 /8 18. In a 3 S state of the helium atom, the possible values of the total electronic angular momentum quantum number are A. 0 only B. 1 only C. 0 and 1 only D. 0, 1/2, and 1 19. Two horizontal scintillation counters are located near the Earth s surface. One is 3.0 meters directly above the other. Of the following, which is the largest scintillator resolving time that can be used to distinguish downward-going relativistic muons from upward-going relativistic muons using the relative time of the scintillator signals? A. 1 picosecond B. 1 nanosecond C. 1 microsecond D. 1 millisecond 20. The ground state of the helium atom is a spin A. singlet B. doublet C. triplet D. quartet 21. U Th He 235 231 2 92 90 4 A uranium nucleus decays at rest into a thorium nucleus and a helium nucleus, as shown above. Which of the following is true? A. Each decay product has the same kinetic energy. B. Each decay product has the same speed. C. The decay products tend to go in the same direction. D. The helium nucleus has more kinetic energy than the thorium nucleus. 22. The configuration of three electrons is 1s2p3p has which of the following as the value of its maximum possible total angular momentum quantum number? A. 7/2 B. 3 C. 5/2 D. 2 23. A beam of electrons is accelerated through a potential difference of 25 kv in an X-ray tube. The continuous X-ray spectrum emitted by the target of the tube will have a short wavelength limit of most nearly A. 0.1 A B. 0.5 A C. 2 A D. 25 A 24. Except for mass, the properties of the muon most closely resemble the properties of the A. electron B. graviton C. photon D. Pion 25. Suppose that _Z^AX decays by natural radioactivity in two stages to _{Z-1}^{A-4}Y. The two stages would most likely be which of the following? First Stage Second Stage A. β emission with an antineutrino α emission B. β emission α emission with a neutrino C. β emission γ emission D. Emission of a deuteron Emission of two neutrons
2. A nickel target (Z = 28) is bombarded with fast electron. The minimum electron kinetic energy needed to produce X-rays in the K-series is most nearly A. 10 ev B. 100 ev C. 1000 ev D. 10,000 ev 27. The configuration of the potassium atom in its ground state is 1s 2 2s 2 2p 3s 2 3p 4s 1. Which of the following statement about potassium is true: A. Its n = 3 shell is completely filled B. Its 4s subshell is completely filled C. Its least tightly bound electron has l = 4 D. Its electron charge distribution is spherically symmetrical 28. Which of the following nuclei has the largest binding energy per nucleon? (Consider the most abundant isotope of each element.) A. Helium B. Carbon C. Iron D. Uranium 29. A proton beam is incident on a scatterer 0.1 centimeter thick. The scatterer contains 10 20 target nuclei per cubic centimeter. In passing through the scatterer, one proton per incident million is scattered. The scattering cross section is A. 10 29 cm² B. 10 27 cm² C. 10 25 cm² D. 10 23 cm² 30. Photons of wavelength λ scatter elastically on free protons initially at rest. The wavelength of the photons scattered at 90 o is increased by A. λ 137 B. λ 183 C. ħ (m e c) where ħ Planck's constant, m e the rest mass of an electron, and c the speed of light D. ħ (m p c) where ħ Planck's constant, m p the rest mass of a proton, and c the speed of light 31. The Franck-Hertz experiment and related scattering experiments show that A. electrons are always scattered elastically from atoms B. electrons are never scattered elastically from atoms C. electrons of a certain energy range can be scattered inelastically, and the energy lost by electrons is discrete D. electron always lose the same energy when they are scattered inelastically 32. Sodium has eleven electrons and the sequence in which energy levels fill in atom is 1s, 2s, 2p, 3s, 3p, 4s, 3d, etc. What is the ground state of sodium in the usual notation 2s+1 L j? A. 1 S 0 B. 2 S 1/2 C. 1 P 0 D. 2 P 1/2 33.
The figure above show the photon interaction cross sections for lead in the energy range where the Compton, photoelectric, and pair production processes all play a role. What is the correct identification of these cross sections? A. 1 = Photoelectric, 2 = Compton, 3 = Pair production B. 1 = Photoelectric, 2 = Pair production, 3 = Compton C. 1 = Compton, 2 = Pair production, 3 = Photoelectric D. 1 = Compton, 2 = Photoelectric, 3 = Pair production 34. An 8-cm diameter by 8-cm long NAI(TI) detector detects gamma rays of a specific energy from a point source of radioactivity. When the source is placed just next to the detector at the center of the circular face, 50 percents of all emitted gamma rays at that energy are detected. If the detector is moved to 1 meter away, the fraction of detected gamma rays drops to A. 10 4 B. 2 10 4 C. 4 10 4 D. 8 10 4 35. The energy required to remove both electrons from the Helium atom in its ground state is 79.0 ev. How much energy is required to ionize Helium (i.e. to remove one electron)? A. 24. ev B. 39.5 ev C. 51.8 ev D. 54.4 ev 3. The primary source of the sun s energy is a series of thermonuclear reactions in which the energy produces is c 2 times the mass difference between A. two hydrogen atoms and one helium atom B. four hydrogen atoms and one helium atom C. six hydrogen atoms and two helium atoms D. three helium atoms and one carbon atom 37. Positronium is an atom formed by an electron and a positron (anti-electron). It is similar to the hydrogen atom, with the positron replacing the proton. If a positronium atom makes a transition from a state with n = 3 to a state with n = 1, the energy of the photon emitted in this transition is closest to A..0 ev B..8 ev C. 12.2 ev D. 13. ev 38. A sample of radioactive nuclei of a certain element can decay only by -emission and -emission. If the half-life for -emission is 24 minutes and that for -emission is 3 minutes, the half-life for sample is A. 30 minutes B. 24 minutes C. 20.8 minutes D. 14.4 minutes 39. The 238 U nucleus has a binding energy of about 7. MeV per nucleon. If the nucleus were to fission into two equal fragments, each would have a kinetic energy of just over 100 MeV. From this it can be concluded that A. 238 U cannot fission spontaneously B. 238 U has a large neutron excess C. nuclei near A = 120 have masses greater than half that of 238 U D. nuclei near A = 120 must be bound by about 8.5 MeV/nucleon 40. When 7 4 Be transforms into 7 3 Li, it does so by A. emitting an alpha particle only B. emitting an electron only
C. emitting a neutron only D. electron capture by the nucleus with the emission of a neutrino 41. The muon decays with a characteristic lifetime of about 10 second into an electron, a muon neutrino, and an electron antineutrino. The muon is forbidden from decaying into an electron and just a single neutrino by the law of conservation of A. charge B. mass C. energy and momentum D. lepton number 42. An energy-level diagram of the n = 1 and n = 2 levels of atomic hydrogen (including the effect of spinorbit coupling and relativity) is shown in the figure. Three transitions are labeled A, B, and C. Which of the transitions will be possible electric-dipole transition? A. B only B. C only C. A and C only D. B and C only 43. The particle decay p must be a weak interaction because A. the is a lepton B. the has spin zero C. no neutrino is produced in the decay D. it does not conserve strangeness 44. What is radius of first Bohr orbit in 208 Pb ( Z 82) for - mesic atom mass of - meson and proton are 207 times and 183 times mass of e 15 A. 3.4 10 m B. 4.3 107m C. 15 3.4 10 m D. 10 0.5 10 m 45. For an ideal Fermi gas in three dimension, the electron velocity V F at the Fermi surface is related to electron concentrations n as 2/3 1/2 1/3 A. VF n B. VF n C. VF n D. VF n 4. If the number of a free electron gas in three dimensions is increased eight times, its Fermi temperature will A. increase by a factor of 4 B. decrease by a factor of 4 C. increases by a factor of 8 D. decreases by a factor of 8 47. Energy expression for a crystal under tight binding is given by 2 2 2 where k k k. x y Density of states near the bottom of the band is 1 1 A. B. 2 2 2 2 4 ak 2 ak 1 C. 2 4 ak 1 D. 2 2 ak x y E( k) E0 2 cos k a cos k a ev
48. Wavelength associated with a moving electron having an energy equal to Fermi energy at absolute zero, varies with particle density as A. 1/3 1/2 B. C. D. 1/3 49. Positronium is an atom formed by an electron and a positron. The mass of a positron is the same as that of an electron and its charge is equal in magnitude but opposite in sign to that of an electron. The positronium atom is thus similar to the hydrogen atom with the positron replacing the proton. The velocity of positronium atom is in ground state. A. 2.18 10 m/ s B. 4.3 10 m/ s C. 2.18 10 m/ s D. none of these 50. How many revolution does an in state of a H-atom make before dropping to state average 8 life time of an excited state is 10 sec A. 8.2 10 B. 8.2 10 C. 2.8 10 D. 2.8 10 ANSWERKEY 1. (d) 2. (a) 3. (c) 4. (a) 5. (b). (b) 7. (b) 8. (c) 9. (a) 10. (c) 11. (d) 12. (a) 13. (c) 14. (a) 15. (c) 1. (d) 17. (d) 18. (b) 19. (b) 20. (a) 21. (d) 22. (a) 23. (b) 24. (a) 25. (a) 2. (d) 27. (d) 28. (c) 29. (c) 30. (d) 31. (c) 32. (b) 33. (b) 34. (c) 35. (a) 3. (b) 37. (a) 38. (d) 39. (d) 40. (d) 41. (d) 42. (d) 43. (d) 44. (a) 45. (d) 4. (a) 47. (a) 48. (d) 49. (c) 50. (a)