Question

Radium having mass number \(200\) and binding energy per nucleon \(5.6\,\text{MeV}\), splits into two fragments Cadmium of mass number \(112\) and Hassium of mass number \(108\). If the binding energy per nucleon for Cadmium and Hassium is approximately \(8.0\,\text{MeV}\), then the energy \(Q\) released per fission will be:

• A. \(598\,\text{MeV}\)
• B. \(176\,\text{MeV}\)
• C. \(640\,\text{MeV}\)
• D. \(475\,\text{MeV}\)

Hint:

In nuclear fission, energy released equals the increase in total binding energy: \(Q = BE_{\text{products}} - BE_{\text{initial}}\).

Answer 1

The Correct Option is C

Step 1: Understand energy released in fission.
The energy released in nuclear fission is equal to the increase in total binding energy of the products compared to the initial nucleus.
\[ Q = \text{Total binding energy of products} - \text{Binding energy of initial nucleus} \]

Step 2: Calculate binding energy of initial radium nucleus.
Given mass number of radium:
\[ A = 200 \]
Binding energy per nucleon:
\[ 5.6\,\text{MeV} \]
So, total binding energy of radium is:
\[ BE_i = 200 \times 5.6 \]
\[ BE_i = 1120\,\text{MeV} \]

Step 3: Calculate total mass number of fragments.
Cadmium has mass number \(112\) and Hassium has mass number \(108\), so:
\[ A_{\text{products}} = 112 + 108 \]
\[ A_{\text{products}} = 220 \]

Step 4: Calculate binding energy of products.
Given binding energy per nucleon of both products is approximately:
\[ 8.0\,\text{MeV} \]
Therefore, total binding energy of products is:
\[ BE_f = 220 \times 8.0 \]
\[ BE_f = 1760\,\text{MeV} \]

Step 5: Find energy released.
\[ Q = BE_f - BE_i \]
\[ Q = 1760 - 1120 \]
\[ Q = 640\,\text{MeV} \]

Step 6: Interpret the result.
Since the final fragments have higher binding energy per nucleon, the products are more stable and the excess energy is released as fission energy.

Step 7: Final answer.
\[ \boxed{640\,\text{MeV}} \]