Question

The atomic mass of $_{6}^{12}C$ is 12.000000 u and that of $_{6}^{13}C$ is 13.003354 u. The required energy to remove a neutron from $_{6}^{13}C$, if mass of neutron is 1.008665 u, will be :

• A. 62.5 MeV
• B. 6.25 MeV
• C. 4.95 MeV
• D. 49.5 MeV

Answer 1

The Correct Option is C

To remove a neutron from \( ^{13}_6C \), the nuclear reaction can be represented as:

\(^{13}_6C \rightarrow ^{12}_6C + \text{neutron}.\)

The mass defect \(\Delta m\) is given by:

\(\Delta m = \left(12.000000 + 1.008665\right) - 13.003354 = -0.00531 \, \text{u}.\)

The energy required for this process is calculated using:

\(E = \Delta m \times 931.5 \, \text{MeV/u}.\)

Substituting values:

\(E = 0.00531 \times 931.5 \approx 4.95 \, \text{MeV}.\)

The Correct answer is: 4.95 MeV