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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Nuclear Physics

NTA Abhyas 2020 · Physics · Nuclear Physics

Li 7 fuses with& a proton& according to the nuclear reaction given...

Li7Li 7 fuses with& a proton& according to the nuclear reaction given below:

p+7Li→4He+4Hep + { }^{7}Li \to { }^{4}He + { }^{4}He

Given that the atomic masses of 1H{}^{1}H, 4He{}^{4}He and 7Li{}^{7}Li are 1.007825u1. 007825u, 4.002603u4. 002603u and 7.016004u7. 016004u respectively, where u=931.5MeV/c2u = 931. 5MeV / c^{2}, then the Q−valueQ - value& of the reaction is

Options

  1. A17.35MeV17. 35MeV
  2. B

    18.06MeV18. 06MeV

  3. C

    177.35MeV177. 35MeV

  4. D

    170.35MeV170. 35MeV

Correct answer

A. 17.35MeV17. 35MeV

Step-by-step solution

The total mass of the initial particles

mi=1.007825+7.016004{m}_{i} = 1. 007825 + 7. 016004

mi=8.023829u{m}_{i} = 8. 023829u

and the total mass of final particles

mf=2×4.002603=8.005206u{m}_{f} = 2 \times 4. 002603 = 8. 005206u

Difference between the initial and final mass of particles

=mi−mf=8.023829−8.005206= {m}_{i} - {m}_{f} = 8. 023829 - 8. 005206

=0.018623u= 0. 018623u

The QQ value is given by

Q=(∆m)c2Q = \left(∆ m\right)c^{2}

=0.018623×931.5=17.35MeV= 0. 018623 \times 931. 5 = 17. 35MeV

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