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Question

Physics Question on Nuclear physics

The atomic mass of 612C_{6}^{12}C is 12.000000 u and that of 613C_{6}^{13}C is 13.003354 u. The required energy to remove a neutron from 613C_{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

4.95 MeV

Explanation

Solution

To remove a neutron from 613C^{13}_6C, the nuclear reaction can be represented as:

613C612C+neutron.^{13}_6C \rightarrow ^{12}_6C + \text{neutron}.

The mass defect Δm\Delta m is given by:

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

The energy required for this process is calculated using:

E=Δm×931.5MeV/u.E = \Delta m \times 931.5 \, \text{MeV/u}.

Substituting values:

E=0.00531×931.54.95MeV.E = 0.00531 \times 931.5 \approx 4.95 \, \text{MeV}.

The Correct answer is: 4.95 MeV