Question

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

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

Hint:

Mass defect is the difference between the expected and actual nuclear mass, and it accounts for the nuclear binding energy.

Answer 1

The Correct Option is C

Mass defect: \[ \Delta m = (12.000000 + 1.008665) - 13.003354 \] \[ = 0.00531 u \] Energy required: \[ E = \Delta m \times 931.5 \] \[ = 0.00531 \times 931.5 \] \[ = 4.95 { MeV} \] Thus, the correct answer is \( 4.95 \) MeV.

Answer 2

Step 1: Understanding the Problem
We are given:

Atomic mass of \( ^{13}_6\text{C} = 13.003354 \, \text{u} \)

Atomic mass of \( ^{12}_6\text{C} = 12.000000 \, \text{u} \)

Mass of neutron \( = 1.008665 \, \text{u} \)

We are to find the energy required to remove one neutron from \( ^{13}\text{C} \).

 

Step 2: Write the Reaction
The process of removing a neutron is represented as: \[ ^{13}_6\text{C} \rightarrow {}^{12}_6\text{C} + n \]

Step 3: Calculate Mass Defect
\[ \Delta m = \left( \text{mass of } ^{12}\text{C} + \text{mass of neutron} \right) - \text{mass of } ^{13}\text{C} \] \[ \Delta m = (12.000000 + 1.008665) - 13.003354 = 13.008665 - 13.003354 = 0.005311 \, \text{u} \]

Step 4: Convert Mass Defect to Energy
We use the relation: \[ E = \Delta m \times 931.5 \, \text{MeV/u} \] \[ E = 0.005311 \times 931.5 = 4.946 \, \text{MeV} \approx 4.95 \, \text{MeV} \]

Final Answer:
\[ \boxed{4.95 \, \text{MeV}} \] Hence, the correct option is:

Option 3: 4.95 MeV