Nuclear Physics | Physics JEE previous year questions with Solutions

Q 1 :
Binding energy of a certain nucleus is $18 \times 10^{8}$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus [2024]

$0.2$ $μ g$
$20$ $μ g$
$10$ $μ g$
$2$ $μ g$

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(B) $Δ m c^{2} = 18 \times 10^{8}$

$Δ m \times 9 \times 10^{16} = 18 \times 10^{8}$

$Δ m = 2 \times 10^{- 8} kg = 20 μ g$

Q 2 :
If $M_{o}$ is the mass of isotope ${}_{5}^{12}B$ , $M_{p}$ and $M_{n}$ are the masses of proton and neutron, then nuclear binding energy of isotope is [2024]

$(M_{o} - 5 M_{p} - 7 M_{n}) C^{2}$
$(M_{o} - 12 M_{n}) C^{2}$
$(M_{o} - 5 M_{p}) C^{2}$
$(5 M_{p} + 7 M_{n} - M_{o}) C^{2}$

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(D) ${}_{5}^{12}B ⟶ 5 p r o t o n + 7 n e u t r o n$

$B . E = Δ m c^{2}$

$(5 M_{p} + 7 M_{n} - M_{o}) c^{2}$

Q 3 :
The energy equivalent of 1 g of substance is: [2024]

$11.2 \times 10^{24} M e V$
$5.6 \times 10^{12} M e V$
$5.6 e V$
$5.6 \times 10^{26} M e V$

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(D) $E = 10^{- 3} \times 9 \times 10^{16} J (∵ E = M c^{2})$

$E = 9 \times 10^{- 13} J$

$1 J = \frac{1}{1.6 \times 10^{- 19}} e V$

$E = 9 \times 10^{13} \times \frac{1}{1.6 \times 10^{- 19}} eV = 5.6 \times 10^{26} MeV$

Q 4 :
The atomic mass of ${}_{6}C^{12}$ is 12.00000u and that of ${}_{6}C^{13}$ is 13.003354u. The required energy to remove a neutron from ${}_{6}C^{13}$ , if mass of neutron is 1.008665u, will be [2024]

62.5 MeV
6.25 MeV
4.95 MeV
49.5 MeV

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(C) ${}_{6}C^{13} + Energy \to {}_{6}C^{12} + {}_{0}n^{1}$

$Δ m = 12 + 1.008665 - 13.003354$

$= - 0.00531 u$

$∴ Energy required = 0.00531 \times 931.5 MeV$

$= 4.95 MeV$

Q 5 :
If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _________ $\times 10^{- 2}$ MeV. (Given 1u = 931 MeV/ $c^{2}$ , atomic mass of helium = 4.002603u). [2024]

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(727) Reaction: $3 {}_{2}^{4}H e \to_{6}^{12} C + Q$

Energy released

$Q = [3 M_{He} - M_{C}] c^{2} = [3 \times 4.002603 - 12] [931]$

$Q = 727 \times 10^{- 2} MeV$

Q 6 :
A star has 100% helium composition. It starts to convert three ${}^{4}H e$ into one ${}^{12}C$ via triple alpha process as ${}^{4}H e + {}^{4}H e + {}^{4}H e \to {}^{12}C + Q$ . The mass of the star is $2.0 \times 10^{32}$ kg and it generates energy at the rate of $5.808 \times 10^{30}$ W. The rate of converting these ${}^{4}H e$ is $n \times 10^{42}$ $s^{- 1}$ , where $n$ is _______ .

[Take, mass of ${}^{4}H e$ = 4.0026 u, mass of ${}^{12}C$ = 12 u] [2024]

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(5) ${}_{2}^{4}H e + {}_{2}^{4}H e + {}_{2}^{4}H e \to {}_{6}^{12}C + Q \Rightarrow 3 {}_{2}^{4}H e \to {}_{6}^{12}C + Q$

$Q = (3 m_{{}^{4}H e} - m_{{}^{12}C}) c^{2}$

$Q = (3 \times 4.0026 - 12) {(3 \times 10^{8})}^{2} = 7.266 MeV$

Power generated $P = \frac{N}{t} Q$ (N = No. of reactions/sec)

$\frac{N}{t} = \frac{P}{Q} = \frac{5.808 \times 10^{30}}{7.266 \times 10^{6} \times 1.6 \times 10^{- 19}} = 5 \times 10^{42}$

Rate of conversion of ${}^{4}H e$ in ${}^{12}C = 5 \times 10^{42}$

Q 7 :
In a nuclear fission process, a high mass nuclide (A $\approx$ 236) with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides (A $\approx$ 118), having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be _______ meV. [2024]

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(236) $Q = B E_{Product} - B E_{Reactant}$

$= 2 (118) (8.6) - 236 (7.6) = 236 \times 1 = 236 MeV$

Q 8 :
The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is $n \times 10^{7}$ kWh, where n = ______. (speed of light = $3 \times 10^{8}$ m/s) [2024]

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(1) $E = Δ m c^{2}$

$= 0.4 \times 10^{- 3} \times {(3 \times 10^{8})}^{2} = 3600 \times 10^{7} kWs$

$= \frac{3600 \times 10^{7}}{3600} kWh = 1 \times 10^{7} kWh$

Topic Question Set

Q 1 :
Binding energy of a certain nucleus is $18 \times 10^{8}$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus [2024]

Q 2 :
If $M_{o}$ is the mass of isotope ${}_{5}^{12}B$ , $M_{p}$ and $M_{n}$ are the masses of proton and neutron, then nuclear binding energy of isotope is [2024]

Q 3 :
The energy equivalent of 1 g of substance is: [2024]

Q 4 :
The atomic mass of ${}_{6}C^{12}$ is 12.00000u and that of ${}_{6}C^{13}$ is 13.003354u. The required energy to remove a neutron from ${}_{6}C^{13}$ , if mass of neutron is 1.008665u, will be [2024]

Q 5 :
If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _________ $\times 10^{- 2}$ MeV. (Given 1u = 931 MeV/ $c^{2}$ , atomic mass of helium = 4.002603u). [2024]

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Q 7 :
In a nuclear fission process, a high mass nuclide (A $\approx$ 236) with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides (A $\approx$ 118), having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be _______ meV. [2024]

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Q 8 :
The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is $n \times 10^{7}$ kWh, where n = ______. (speed of light = $3 \times 10^{8}$ m/s) [2024]

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Topic Question Set

Q 1 : Binding energy of a certain nucleus is 18×108J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus [2024]

Q 2 : If Mo is the mass of isotope B512, Mp and Mn are the masses of proton and neutron, then nuclear binding energy of isotope is [2024]

Q 3 : The energy equivalent of 1 g of substance is: [2024]

Q 4 : The atomic mass of C126 is 12.00000u and that of C136 is 13.003354u. The required energy to remove a neutron from C136, if mass of neutron is 1.008665u, will be [2024]

Q 5 : If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _________ ×10-2 MeV. (Given 1u = 931 MeV/c2, atomic mass of helium = 4.002603u). [2024]

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Q 7 : In a nuclear fission process, a high mass nuclide (A ≈ 236) with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides (A ≈ 118), having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be _______ meV. [2024]

0%

Q 8 : The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is n×107 kWh, where n = ______. (speed of light = 3×108 m/s) [2024]

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Q 1 :
Binding energy of a certain nucleus is $18 \times 10^{8}$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus [2024]

Q 2 :
If $M_{o}$ is the mass of isotope ${}_{5}^{12}B$ , $M_{p}$ and $M_{n}$ are the masses of proton and neutron, then nuclear binding energy of isotope is [2024]

Q 3 :
The energy equivalent of 1 g of substance is: [2024]

Q 4 :
The atomic mass of ${}_{6}C^{12}$ is 12.00000u and that of ${}_{6}C^{13}$ is 13.003354u. The required energy to remove a neutron from ${}_{6}C^{13}$ , if mass of neutron is 1.008665u, will be [2024]

Q 5 :
If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _________ $\times 10^{- 2}$ MeV. (Given 1u = 931 MeV/ $c^{2}$ , atomic mass of helium = 4.002603u). [2024]

Q 7 :
In a nuclear fission process, a high mass nuclide (A $\approx$ 236) with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides (A $\approx$ 118), having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be _______ meV. [2024]

Q 8 :
The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is $n \times 10^{7}$ kWh, where n = ______. (speed of light = $3 \times 10^{8}$ m/s) [2024]