Topic: Early Atomic Structure
1. Rutherford’s atomic model could account for
4. Radius of \( ^4_2\text{He} \) nucleus is 3 fermi. The radius of \( ^{206}_{82}\text{Pb} \) nucleus will be
7. An alpha nucleus of energy bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
9. An \( \alpha \) particle of energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of the closest approach is of the order of
Topic: Bohr’s Modal Spectrum
2. Energy required for the electron excitation in \( \text{Li}^{2+} \) from the first to the third Bohr orbit is
3. When an electron jumps from the orbit n = 2 to n = 4, then wavelength of the radiations absorbed will be (R is Rydberg’s constant)
5. In an inelastic collision an electron excites a hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-state and ionizes it. At least how much energy the second electron transfers to the atom is the M-state ?
8. \( \nu_1 \) is the frequency of the series limit of Lyman series, \( \nu_2 \) is the frequency of the first line of Lyman series and \( \nu_3 \) is the frequency of the series limit of the Balmer series. Then
11. The wavelength of radiation emitted is \( \lambda_0 \) when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit of hydrogen atom, the wavelength of radiation emitted will be
13. The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to \( n^x \), where x is
15. Of the following transitions in the hydrogen atom, the one which gives an emission line of the highest frequency is
17. The energy of electron in the nth orbit of hydrogen atom is expressed as \( E_n = -\frac{13.6}{n^2} \text{ eV} \). The shortest and longest wavelength of Lyman series will be
18. The acceleration of electron in the first orbit of hydrogen atom is
22. Which of the following transition gives the photon of minimum frequency ?
24. In the Bohr’s model of the hydrogen atom, the lowest orbit corresponds to
28. Which of the following lines of the H-atom spectrum belongs to the Balmer series ?
30. The radius of hydrogen atom in its ground state is \( 5.3 \times 10^{-11} \text{ m} \). After collision with an electron it is found to have a radius of \( 21.2 \times 10^{-11} \text{ m} \). What is the principal quantum number n of the final state of atom ?
33. If the radii of nuclei of \( ^{27}_{13}\text{Al} \) and \( ^{64}_{30}\text{Zn} \) are \( R_1 \) and \( R_2 \) respectively, then \( \frac{R_1}{R_2} \) is equal to
36. The ratio of areas of the electron orbits for the first excited state and the ground state for the hydrogen atom is
38. According to Bohr’s theory of hydrogen atom, for the electron in the nth allowed orbit the
(i) linear momentum is proportional to 1/n
(ii) radius is proportional to n
(iii) kinetic energy is proportional to \( 1/n^2 \)
(iv) angular momentum is proportional to n
Choose the correct option from the codes given below.
40. The spin-orbit interaction has no effect in the level of the hydrogen atom
44. The ratio of minimum wavelengths of lyman and Balmer series will be
47. The ionisation potential of hydrogen atom is –13.6 eV. An electron in the ground state of a hydrogen atoms absorbs a photon of energy 12.75 eV. How many different spectrial line can one expect when the electron make a downward transition ?
50. The first excitation potential of a given atom is 10.2 V. Then, ionisation potential must be
55. The diagram shows the energy levels for an electron in a certain atom. Which transition whown represents the emission of a photon with the most energy ?
57. Electrons in a certain energy level \( n = n_1 \), can emit 3 spectral lines. When they are in another energy level, \( n = n_2 \), they can emit 6 spectrial lines. The orbital speed of the electrons in the orbits are in the ratio
59. Three photons coming from excited atomic hydrogen sample are observed, their energies are 12.1 eV, 10.2 eV and 1.9 eV. These photons must come from
61. The K line of singly ionised calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, the spectral line is located at 401.8 nm. The speed with which this galaxy is moving away from us, will be
65. Ionization potential of hydrogen atom is 13.6 eV hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr’s theory, the spectral lines emitted by hydrogen will be
66. If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of \( \text{Li}^{2+} \) is
69. Energy E of a hydrogen atom with principal quantum number n is given by \( E_n = -\frac{13.6}{n^2} \text{ eV} \). The energy of a photon ejected when the electron jumps from n = 3 state to n = 2 state of hydrogen, is approximately
75. In hydrogen atom, the electron is moving round the nucleus with velocity \( 2.18 \times 10^6 \text{ ms}^{-1} \) in an orbit of radius 0.528 Å. The acceleration of the electron is
78. At the time of total solar eclipse, the spectrum of solar radiation will have
80. Electrons in the atom are held to the nucleus by
84. Bohr’s atom model assumes
91. Band spectrum is also called
94. The first excited state of hydrogen atom is 10.2 eV above its ground state. The temperature needed to excite hydrogen atoms to first excited level, is
97. The electric potential between a proton and an electron is given by \( V = V_0 \ln(r/r_0) \), where \( r_0 \) is a constant. Assuming Bohr’s model to be applicable, write variation of \( r_n \) with n, n being the principal quantum number ?
101. The ratio of the wavelengths for 2→1 transition in \( \text{Li}^{2+} \), \( \text{He}^{+} \) and H is
103. The ionisation potential of mercury is 10.39 V. How far an electron must travel in an electric field of \( 1.5 \times 10^6 \text{ Vm}^{-1} \) to gain sufficient energy to ionize mercury ?
107. If the electron in hydrogen atom jumps from the third to second orbit, the wavelength of the emitted radiation in terms of Rydberg constant R is given by
Topic: Atomic nucleus and Nuclear Reactions
2. After absorbing a slowly moving neutron of mass \( m_N \) (momentum 0) a nucleus of mass M breaks into two nuclei of masses \( m_1 \) and \( 5m_1 \) (\( 6m_1 = M + m_N \)), respectively. If the de-Broglie wavelength of the nucleus with mass \( m_1 \) is \( \lambda \), then de-Broglie wavelength of the other nucleus will be
5. In the nuclear reaction \( ^{14}_{7}\text{N} + ^{1}_{1}\text{H} \rightarrow \text{X} + ^{14}_{6}\text{C} \), the X will be
7. Atomic weight of boron is 10.81 and it has two isotopes \( ^{10}_{5}\text{B} \) and \( ^{11}_{5}\text{B} \). Then ratio of \( ^{10}_{5}\text{B} : ^{11}_{5}\text{B} \) in nature would be
10. \( ^{238}_{92}\text{U} \) has 92 protons and 238 nucleons. It decays by emitting an alpha particle and becomes
11. Which one of the following is a possible nuclear reaction ?
14. \( ^{235}_{92}\text{U} \) undergoes successive disintagrations with the end product of \( ^{203}_{82}\text{Pb} \). The number of \( \alpha \) and \( \beta \)-particles emitted are
16. In the reaction \( ^{14}_{7}\text{N} + \alpha \rightarrow \text{X} + ^{1}_{1}\text{P} \), identify X.
17. A certain radioactive material \( ^{A}_{Z}\text{X} \) starts emitting \( \alpha \) and \( \beta \) particles successively such that the end product is \( ^{A-8}_{Z-3}\text{Y} \). The number of \( \alpha \) and \( \beta \) particles emitted are
19. If \( M_0 \) is the mass of an oxygen isotope \( ^{17}_{8}\text{O} \), \( M_p \) and \( M_n \) are the masses of a proton and a neutron, respectively, the nuclear binding energy of the isotope is
23. The nucleus \( ^{12}_{6}\text{C} \) absorbs an energetic neutron and emits a beta particle (\( \beta \)). The resulting nucleus is
26. In gamma ray emission from a nucleus
27. The volume of a nucleus is directly proportional to
31. \( ^{14}_{7}\text{N} \) is bombarded with \( ^{4}_{2}\text{He} \). The resulting nucleus is \( ^{17}_{8}\text{O} \) with the emission of
33. A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be
35. \( m_p \) and \( m_n \) are masses of proton and neutron respectively. An element of mass M has Z protons and N neutrons then
37. The radius of a nucleus with atomic mass number 7 is 2 fermi. Find the radius of nucleus with atomic number 189.
40. If the binding energy per nucleon in \( ^{7}_{3}\text{Li} \) and \( ^{4}_{2}\text{He} \) nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction \( ^{7}_{3}\text{Li} + ^{1}_{1}\text{p} \rightarrow 2 ^{4}_{2}\text{He} \), energy of proton must be
41. Calculate the energy released when three \( \alpha \)-particles combined to from a \( ^{12}\text{C} \) nucleus, the mass defect is (atomic mass of \( ^{4}_{2}\text{He} \) is 4.002603 u)
43. The binding energy per nucleon for deuteron and helium are 1.1 MeV and 7.0 MeV. The energy released when two deuterons fuse to form a helium nucleus is
46. If \( ^{236}_{92}\text{U} \) emits 8 \( \alpha \)-particles and 6 \( \beta \)-particles, then the resulting nucleus is
52. Two nucleons are at a separation of one fermi, protons have a charge of \( +1.6 \times 10^{-19} \text{ C} \). The net nuclear force between them is \( F_1 \), if both are neutrons, \( F_2 \) if both are protons and \( F_3 \) if one is proton and the other is neutron. Then
57. Consider the following two statements A and B and identify the correct answer given
A : Nuclear density is same for all nuclei
B : Radius of the nucleus R and its mass the number A are related as
59. The energy equivalent to a kilogram of matter is about
62. The density of uranium is of the order of
63. The mass defect in a particular nuclear reaction if 0.3 g. The amount of energy liberated in kilowatt hour is (Velocity of light = \( 3 \times 10^8 \text{ ms}^{-1} \))
Topic: Radioactivity
2. The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is
4. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is
5. The radioactivity of a simple is \( I_1 \) at a time \( t_1 \) and \( I_2 \) at a time \( t_2 \). If the half-life of the sample is \( \tau_{1/2} \), then the number of nuclei that have disintegrated in the time \( t_2 - t_1 \) is proportional to
7. A radioactive nucleus (initial mass number A and atomic number Z) emits 3 \( \alpha \)-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
8. A radioactive sample S1 having the activity A1 has twice the number of nuclei as another sample S2 of activity A2. If A2= 2A1, then the ratio of half-life of S1 to the half-life of S2 is
13. Consider an initially pure 3.4 g sample of \( ^{67}\text{Ga} \), an isotope that has a half-life of 78 h. What is its initial decay rate ?
14. If the decay constant of a radioactive substance is \( \lambda \), then its half-life is
17. In \( \beta^+ \) decay process, the following changes take place inside the nucleus
20. In a radioactive disinategration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mena life is
23. Half-life of radioactive sample, when activity of material initially was 8 counts and after 3 h it becomes 1 count, is
24. Which shows radioactivity ?
25. \( ^{235}_{92}\text{X} \rightarrow ^{231}_{91}\text{Y} \). Number of particle emitted in the reaction is
26. The end product of the decay of \( ^{232}_{90}\text{Th} \) is \( ^{208}_{82}\text{Pb} \). The number of \( \alpha \) and \( \beta \)-particles emitted are respectively
29. A radioactive sample S1 having an activity of 5mCi has twice the number of nuclei as another sample S2 which has an activity of 10mCi. The half lives of S1 and S2 can be
30. The fossil bone has a \( ^{14}\text{C} : ^{12}\text{C} \) ratio, which is \( \frac{1}{16} \) of that in a living animal bone. If the half-life of \( ^{14}\text{C} \) is 5730 yr, then the age of the fossil bone is
32. Two radioactive substances A and B have decay constants \( 5\lambda \) and \( \lambda \) respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be \( (1/e)^2 \) after a time interval
34. Mass spectrometric analysis of potassium and argon atoms in a Moon rock sample shows that the ratio of the number of (stable)\( ^{40}\text{Ar} \) atoms present to the number of (radioactive)\( ^{40}\text{K} \) atoms is 10.3 Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of \( 1.25 \times 10^9 \text{ yr} \). How old is the rock ?
63. The half-life of radon is 3.8 days. How many radon will be left out of 1024 mg after 38 days
65. A radioactive nucleus A finally transforms into a stable nucleus B. Then A and B can be
67. Starting with a sample of pure \( ^{66}\text{Cu} \), 7/8 of it decays into Zn in 15 min. The corresponding half-life is
70. The counting rate observed from a radioactive source at t = 9s was 1600 count s–1 and at t = 8 s it was 100 counts s–1. The counting rate observed as counts per second at t = 6s, will be
73. A hypothetical radioactive nucleus decays according to the following series
\( A \xrightarrow{\alpha} A_1 \xrightarrow{\beta} A_2 \xrightarrow{\alpha} A_3 \xrightarrow{\gamma} A_4 \)
If the mass number and atomic number of A are respectively 180 and 72. Then to atomic number and mass number of \( A_4 \) will respectively be
76. \( ^{14}\text{C} \) has half-life 5700 year. At the end of 11400 years, the actual amount left is
78. For thorium A = 232, Z = 90 at the end of some radioactive desintegration we obrain an isotope of lead with A = 208 and Z = 82, then the number of emitted \( \alpha \) and \( \beta \) particles are
79. Two radioactive nuclides x and y have half-live 1 h and 2 h respectively. Initally the samples have equal number of nuclei. After 4 h the ratio of the numbers of x and y is
Topic: Nuclear Fission and Fusion
1. The binding energy per nucleon for the parent nucleus is \( E_1 \) and that for the daughter nuclei is \( E_2 \). Then
3. Assume the graph of specific binding energy verses mass number is as shown in the figure. Using this graph, select the correct choice from the following.
4. Pick out the correct statement from the following.
6. A \( ^{238}_{92}\text{U} \) nucleus at rest is decayed by emitting alpha particle into \( ^{234}_{90}\text{Th} \). The speeds of the alpha particle and the thorium nucleus are in the ratio
9. \( F_{pe} \) represents electrical force on proton due to electron and \( F_{ep} \) on electron due to proton in a hydrogen atom. Similarly \( F_{pe} \) represents the gravitational force on proton due to electron and \( F_{ep} \) the corresponding force on electron due to proton. Which of the following is not true ?
10. Using the following data
Mass of hydrogen atom = 1.00783 u
Mass of neutron = 1.00867 u
Mass of nitrogen atom (\( ^{14}_{7}\text{N} \)) = 14.00307 u
The calculated value of the binding energy of the nucleus of the nitrogen atom (\( ^{14}_{7}\text{N} \)) is close to
14. Two protons are kept at a separation of 40 Å. \( F_n \) is the nuclear force and \( F_e \) is the electrostatic force between them. Then
15. On bombarding \( \text{U}^{235} \) by slow neutron, 200 MeV energy is released. If the power output of atomic reactor is 1.6 MW, then the rate of fission will be
18. In any fission process the ratio \( \frac{\text{mass of fission products}}{\text{mass of parent nucleus}} \) is
19. The nuclear fusion reaction is given \( ^{2}_{1}\text{H} + ^{2}_{1}\text{H} \rightarrow ^{3}_{0}\text{He} + ^{1}_{0}\text{n} + Q \) (energy). If 2 mole of deuterium are fused the total released energy is
22. Consider the nuclear reaction \( \text{X}^{200} \rightarrow \text{A}^{110} + \text{B}^{80} \). If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.1 MeV respectively, then the energy released in the reaction is
24. If 200 MeV energy is released in the fission of a single nucleus of \( ^{235}_{92}\text{U} \). How many fissions must occur per second to produce a power of 1 kW ?
30. The fussion process is possible at high temperature, because at higher temperatures
36. When \( ^{235}_{92}\text{U} \) is bombarded with one neutron, fission occurs and the products are three neutrons, \( ^{94}_{36}\text{Kr} \), and
40. An atomic power nuclear reactor can deliver 300 MW. The energy released due to fission of each nucleus of uranium atom \( \text{U}^{238} \) is 170 MeV. The number of uranium atoms fissioned per hour will be
41. In the nuclear fusion reaction,
\( ^{2}_{1}\text{H} + ^{3}_{1}\text{H} \rightarrow ^{4}_{2}\text{He} + \text{n} \)
given that the repulsive potential energy between the two nuclei is \( 7.7 \times 10^{-14} \text{ J} \), the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann’s constant \( k = 1.38 \times 10^{-23} \text{ JK}^{-1} \)]
42. In a nuclear reactor, the fuel is consumed at the rate of \( 1 \text{ mgs}^{-1} \). The power generated in kilowatt is