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The Nucleus — JEE Main & Advanced Physics PYQs

110 previous year questions from The Nucleus with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

110 questionsPhysicsSolutions on every page
1

A neutron star possesses a density equivalent to that of nuclear matter. Assuming the star is spherical, determine the radius of a neutron star with a mass of 4.0 10³⁰ kg (twice th

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2

Determine the amount of energy released during the reaction given below: ⁷ Li + p + . The atomic mass of ⁷ Li is 7.0160 u and that of ⁴ He is 4.0026 u .

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3

Determine the binding energy per nucleon of ¹⁹⁷₇₉ Au , given that its atomic mass is 196.96 u .

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4

Compute the energy released if an -particle is emitted by ²³⁸ U . The atomic masses of ²³⁸ U , ²³⁴ Th , and ⁴ He are 238.0508 u , 234.04363 u , and 4.00260 u respectively.

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5

Suppose that the mass of a nucleus is roughly given by M = A m_p , where A represents the mass number. Estimate the density of matter inside a nucleus in kg m ⁻³ , and determine th

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6

Determine the mass of an -particle, given that its binding energy is 28.2 MeV .

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7

Compute the energy that needs to be supplied to ²³⁸ U in order for two protons and two neutrons to be emitted one by one. The atomic masses of ²³⁸ U , ²³⁴ Th , and ⁴ He are 238.050

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8

Calculate the energy released in the nuclear reaction ²²³ Ra ²⁰⁹ Pb + ¹⁴ C . The necessary atomic masses are provided below. ²²³ Ra ²⁰⁹ Pb ¹⁴ C 223.018 u 208.981 u 14.003 u

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9

Evaluate the minimum energy required to separate a proton from a nucleus containing Z protons and N neutrons. Let M_ Z, N denote the mass of an atom with Z protons and N neutrons i

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10

Determine the minimum energy required to separate a neutron from a nucleus containing Z protons and N neutrons, in terms of the masses M_ Z, N , M_ Z, N-1 , and the mass of the neu

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11

³² P undergoes beta-decay to ³² S . Calculate the sum of the energy of the antineutrino and the kinetic energy of the -particle. Disregard the recoil of the daughter nucleus. The a

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12

A free neutron undergoes beta-decay to a proton, having a half-life of 14 minutes . Determine the decay constant.

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13

A free neutron undergoes beta-decay to a proton, having a half-life of 14 minutes . Calculate the energy liberated during this process.

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14

Determine the missing product to complete the given decay scheme: ²²⁶₈₈ Ra + ,?

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15

Determine the missing products to complete the given decay scheme: ¹⁹₈ O ¹⁹₉ F + ,?

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16

Determine the missing products to complete the given decay scheme: ²⁵₁₃ Al ²⁵₁₂ Mg + ,?

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17

In the decay ⁶⁴ Cu ⁶⁴ Ni + e⁺ + , the maximum kinetic energy carried by the positron is observed to be 0.650 MeV . Determine the energy of the neutrino that is emitted alongside a

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18

In the decay ⁶⁴ Cu ⁶⁴ Ni + e⁺ + , the maximum kinetic energy carried by the positron is observed to be 0.650 MeV . Determine the momentum of the neutrino in kg m s ⁻¹ if it is emit

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19

Potassium-40 can decay in three modes. It can decay via ⁻ -emission, ⁺ -emission or electron capture. Determine the equations showing the end products for these three modes respect

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20

Potassium-40 can decay in three modes: ⁻ -emission, ⁺ -emission or electron capture. The atomic masses of ⁴⁰₁₈ Ar , ⁴⁰₁₉ K and ⁴⁰₂₀ Ca are 39.9624 u , 39.9640 u and 39.9626 u respe

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21

Lithium ( Z = 3 ) possesses two stable isotopes, ⁶ Li and ⁷ Li . When a lithium sample is bombarded with neutrons, electrons and -particles are ejected. Identify the correct set of

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22

Determine the maximum energy that a positron can possess during the ⁺ -decay of ¹¹ C into ¹¹ B . The atomic masses of ¹¹ C and ¹¹ B are 11.0114 u and 11.0093 u , respectively.

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23

A ²²⁸ Th nucleus emits an alpha particle, reducing to ²²⁴ Ra . Calculate the kinetic energy of the alpha particle emitted during the following decay: ²²⁸ Th ²²⁴ Ra ^ * + ²²⁴ Ra ^ *

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24

Determine the maximum kinetic energy of the beta particle emitted during the following decay scheme: ¹² N ¹² C ^ * + e⁺ + ¹² C ^ * ¹² C + ;(4.43 MeV ) . The atomic mass of ¹² N is

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25

The decay constant of ¹⁹⁷₈₀ Hg (which decays by electron capture to ¹⁹⁷₇₉ Au ) is 1.8 10⁻⁴ s ⁻¹ . What is the half-life of this isotope?

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26

The decay constant of ¹⁹⁷₈₀ Hg (which decays by electron capture to ¹⁹⁷₇₉ Au ) is 1.8 10⁻⁴ s ⁻¹ . Determine the average-life of this isotope.

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27

The decay constant of ¹⁹⁷₈₀ Hg (which decays by electron capture to ¹⁹⁷₇₉ Au ) is 1.8 10⁻⁴ s ⁻¹ . How much time is needed to convert 25 % of this mercury isotope into gold?

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28

Given that the half-life of ¹⁹⁸ Au is 2.7 days , determine the activity of a sample which contains 1.00 g of ¹⁹⁸ Au . Consider the atomic weight of ¹⁹⁸ Au to be 198 g mol ⁻¹ .

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29

Determine the activity of a sample containing initially 1.00 g of ¹⁹⁸ Au after 7 days have elapsed. The half-life of ¹⁹⁸ Au is 2.7 days and its atomic weight is 198 g mol ⁻¹ .

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30

A sample containing radioactive ¹³¹ I with a half-life of 8.0 days has an initial activity of 20 Ci at t = 0 . Determine the activity of the sample at t = 4.0 days .

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31

A sample containing radioactive ¹³¹ I with a half-life of 8.0 days has an initial activity of 20 Ci at t = 0 . Find the decay constant of the sample at t = 4.0 days .

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32

Given that the decay constant of ²³⁸ U is 4.9 10⁻¹⁸ s ⁻¹ , find the half-life of ²³⁸ U .

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33

The decay constant for ²³⁸ U is 4.9 10⁻¹⁸ s ⁻¹ . Determine the average-life of ²³⁸ U .

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34

The decay constant of ²³⁸ U is 4.9 10⁻¹⁸ s ⁻¹ . By what factor will the activity of a ²³⁸ U sample decrease in 9 10⁹ years ?

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35

At a certain time, a specific sample of a radioactive material decays at the rate of 500 per second. After 50 minutes , the count rate falls to 200 per second. Determine the decay

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36

At a certain time, a specific sample of a radioactive material decays at the rate of 500 per second. After 50 minutes , the count rate falls to 200 per second. Determine the half-l

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37

The half-life of ²²⁶ Ra is 1602 y . Determine the activity of 0.1 g of RaCl ₂ , assuming all the radium present is in the form of ²²⁶ Ra . Consider the atomic weight of Ra to be 22

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38

Over a duration of 20 hours , the count rate from a radioactive sample drops from 4.0 10⁶ per second to 1.0 10⁶ per second. Calculate the count rate 100 hours after the initial ins

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39

A radioisotope has a half-life of 10 h . Determine the total number of disintegrations that occur in the tenth hour, measured from a time when the activity was 1 Ci .

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40

The selling rate of a radioactive isotope is determined by its activity. What will be the second-hand rate of a one month old ³² P ( t_ 1/2 = 14.3 days ) source if it was initially

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41

By ⁺ -emission, ⁵⁷ Co decays into ⁵⁷ Fe . The produced ⁵⁷ Fe is initially in an excited state and transitions to the ground state by emitting -rays. The half-life for the ⁺ -decay

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42

Carbon ( Z = 6 ) possessing mass number 11 decays into boron ( Z = 5 ). Identify the type of decay taking place.

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43

Carbon ( Z = 6 ) possessing mass number 11 decays into boron ( Z = 5 ). The half-life for this decay scheme is 20.3 minutes . Calculate the time elapsed before a mixture containing

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44

A vessel contains 4 10²³ tritium atoms. Given that the half-life for the decay of tritium nuclei is 12.3 y , determine the activity of the sample.

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45

A vessel holds 4 10²³ tritium atoms. If the half-life for the decay of tritium nuclei is 12.3 y , calculate the number of decays taking place in the subsequent 10 hours .

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46

Inside a vessel, there are 4 10²³ tritium atoms. The half-life for the decay of tritium nuclei is 12.3 y . Evaluate the number of decays that will occur over the next 6.15 y .

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47

A point source emitting alpha particles is situated at a distance of 1 m from a counter that registers any alpha particle striking its 1 cm ^2 window. Given that the source has 6.0

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48

Charcoal prepared from a living tree exhibits a disintegration rate of 15.3 disintegrations of ¹⁴ C per gram per minute. An ancient charcoal sample has a ¹⁴ C activity of 12.3 disi

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49

Natural water contains a trace amount of tritium ( ³₁ H ). This isotope beta-decays with a half-life of 12.5 years . While ascending a difficult peak, a mountaineer discovers debri

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50

²³⁸ U decays to ²⁰⁶ Pb with a half-life of 4.47 10⁹ y through a chain of processes. A rock sample is discovered to contain 2.00 mg of ²³⁸ U and 0.600 mg of ²⁰⁶ Pb . Assuming that a

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51

The count rate of nuclear radiation emitted from a radioactive sample containing ¹²⁸ I varies with time in the following manner. Time t (minute) 0 25 50 75 100 Count rate R ( 10⁹ s

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52

For a radioactive sample containing ¹²⁸ I , let R₀ be the initial count rate and R be the count rate of the nuclear radiation at time t . What is the nature of the plot of (R₀/R) a

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53

The decay constant for a radioactive sample containing ¹²⁸ I is found to be approximately 0.028 min ⁻¹ . Calculate the half-life t_ 1/2 . Time t (minute) 0 25 50 75 100 Count rate

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54

The half-life of ⁴⁰ K is 1.30 10⁹ y . A 1.00 g sample of pure KCl yields 160 counts s ⁻¹ . Determine the relative abundance of ⁴⁰ K (the fraction of ⁴⁰ K present) in natural potass

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55

¹⁹⁷₈₀ Hg decays to ¹⁹⁷₇₉ Au via electron capture, with a decay constant of 0.257 per day. Determine the other particle or particles that are emitted in this decay.

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56

¹⁹⁷₈₀ Hg decays to ¹⁹⁷₇₉ Au via electron capture, with a decay constant of 0.257 per day. Assuming the captured electron comes from the K shell, determine the wavelength of the K_

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57

In an experiment, a radioactive isotope is produced at a constant rate dN/dt = R . The isotope has a half-life t_ 1/2 . After a time t t_ 1/2 , the number of active nuclei becomes

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58

In an experiment, a radioactive isotope is generated at a constant rate dN/dt = R . The isotope has a half-life t_ 1/2 . Assuming that the generation of the radioactive isotope beg

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59

During an agricultural experiment, a solution containing 1 mole of a radioactive material ( t_ 1/2 = 14.3 days ) was injected into the roots of a plant. The plant was left to settl

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60

A vessel with a volume of 125 cm ^3 holds tritium ( ³ H , t_ 1/2 = 12.3 y ) gas at a pressure of 500 kPa and a temperature of 300 K . Determine the activity of the gas.

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61

The nuclide ²¹²₈₃ Bi is capable of disintegrating by emitting either an -particle or a ⁻ -particle. Identify the correct pair of equations showing the products of these two decay m

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62

The nuclide ²¹²₈₃ Bi is capable of disintegrating by emitting either an -particle or a ⁻ -particle. The probabilities for disintegration via - and -decays stand in the ratio 7/13 .

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63

A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹

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64

A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹

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65

A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹

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66

A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹

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67

A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹

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68

A human body eliminates certain substances following a law analogous to radioactive decay. When technetium is administered to a human body in some chemical form, half of the substa

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69

A charged capacitor with capacitance C undergoes discharge through a resistance R . Simultaneously, a radioactive sample decays with an average-life . Determine the value of R such

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70

In a nuclear physics experiment, radioactive isotopes are produced at a constant rate dN/dt = R . A series circuit is formed by connecting an inductor of inductance 100 mH , a resi

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71

Determine the energy released by 1 g of natural uranium, given that each fission event releases 200 MeV and the fissionable isotope ²³⁵ U constitutes 0.7 % by weight in natural ura

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72

A uranium reactor generates thermal energy at a rate of 300 MW . Determine the amount of ²³⁵ U consumed every second, given that the average energy released per fission is 200 MeV

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73

A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25 % f

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74

A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25 % f

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75

A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25 % f

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76

Determine the Q -value for the fusion reaction: ²₁ H + ²₁ H ³₁ H + ¹₁ H Atomic masses are given as m(²₁ H ) = 2.014102 u , m(³₁ H ) = 3.016049 u , m(³₂ He ) = 3.016029 u , and m(⁴₂

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77

Determine the Q -value for the fusion reaction: ²₁ H + ²₁ H ³₂ He + n Atomic masses are given as m(²₁ H ) = 2.014102 u , m(³₁ H ) = 3.016049 u , m(³₂ He ) = 3.016029 u , and m(⁴₂ H

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78

Determine the Q -value for the fusion reaction: ²₁ H + ³₁ H ⁴₂ He + n Atomic masses are given as m(²₁ H ) = 2.014102 u , m(³₁ H ) = 3.016049 u , m(³₂ He ) = 3.016029 u , and m(⁴₂ H

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79

Consider fusion occurring in a helium plasma. Determine the temperature at which the average thermal energy, given by 1.5 kT , becomes equal to the Coulomb potential energy at a se

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80

Determine the Q -value for the fusion reaction ⁴ He + ⁴ He ⁸ Be , and indicate whether this process is energetically favourable. The atomic mass of ⁸ Be is given as 8.0053 u , whil

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81

Determine the energy that can be extracted from 1 kg of water via the fusion reaction ² H + ² H ³ H + p . Assume that 1.5 10⁻² % of natural water consists of heavy water D ₂ O (by

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82

For a neutral carbon atom in its ground state, the mass is

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83

The mass number of a nucleus is equivalent to

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84

In comparison to the ¹² C atom, the ¹⁴ C atom possesses

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85

The mass number of an atomic nucleus is

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86

Suppose F_ pp , F_ pn , and F_ nn represent the magnitudes of the nuclear force exerted by a proton on a proton, a proton on a neutron, and a neutron on a neutron, respectively. Fo

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87

For a nucleus having radius R and mass number A , the plot of (R/R₀) against A is

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88

Consider F_ pp , F_ pn , and F_ nn as the magnitudes of the net force exerted by a proton on a proton, by a proton on a neutron, and by a neutron on a neutron, respectively. Disreg

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89

Two protons are positioned at a separation of 10 nm . Let F_n and F_e denote the nuclear force and the electromagnetic force between them, respectively. Which of the following is t

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90

With an increase in the mass number A , the binding energy per nucleon of a nucleus

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91

During a single average-life,

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92

Which of the following statements provides an incorrect description of the binding energy of a nucleus?

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93

During a radioactive decay process, both the atomic number and the mass number remain unchanged. Identify the particle that is emitted in this decay.

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94

In the process of negative beta decay,

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95

A newly prepared radioactive source with a half-life of 2 h emits radiation at an intensity 64 times the allowable safe level. The minimum time required before one can safely work

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96

A radioactive sample has a decay constant . The half-life and average-life of the sample are respectively

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97

Free ²³⁸ U nuclei placed inside a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures the separation between the alpha parti

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98

Ten grams of ⁵⁷ Co is placed in an open container and undergoes beta-decay with a half-life of 270 days . After 540 days , the weight of the material inside the container will be a

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99

When a ¹⁴ N nucleus is bombarded with an -particle, a ¹⁷ O nucleus is produced along with the emission of another particle. The emitted particle is a

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100

In a nuclear fission reaction,

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101

Heavier nuclei tend to exhibit a larger N/Z ratio because

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102

When the mass number A of a nucleus increases, which of the following associated quantities remains unchanged?

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103

A free neutron decays into a proton, but a free proton does not decay into a neutron. This happens because

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104

Consider a sample of pure beta-active material.

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105

In which of the following decay processes does the element remain unchanged?

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106

Which of the following decays result in a decrease in the atomic number?

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107

A magnetic field fails to cause deflection in

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108

Which among the following are electromagnetic waves?

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109

In the case of nuclei having A > 100 ,

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110

In a lithium vapour at room temperature, two lithium nuclei do not combine to form a carbon nucleus because

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