The disintegration energy Q for the nuclear fission of ^235 U arrow ^140 Ce+ ^94 Zr+n is \underline\hspace2cmMeV . Given atomic masses of ^235 U: 235.0439 u ; ^140 Ce: 139.9054 u, ^94 Zr: 93.9063 u ; n: 1.0086 u , Value of c^2=931 ~MeV / u .

Atoms and Nuclei PYQ — JEE Main 2024 · 4 Apr · Shift 2 · Q85 with Solution

View written solutionFree

Correct answer: 208

\mathrm{U} \rightarrow \, ^{140}\mathrm{Ce} + \, ^{94}\mathrm{Zr} + n$$ The disintegration energy is $$Q = \left( m_{\text{initial}} - m_{\text{final}} \right)c^2$$ 2. **Initial mass** Given: $$m(^{235}\mathrm{U}) = 235.0439\,u$$ So, $$m_{\text{initial}} = 235.0439\,u$$ 3. **Final mass** Given: $$m(^{140}\mathrm{Ce}) = 139.9054\,u$$ $$m(^{94}\mathrm{Zr}) = 93.9063\,u$$ $$m(n) = 1.0086\,u$$ Hence, $$m_{\text{final}} = 139.9054 + 93.9063 + 1.0086$$ $$m_{\text{final}} = 234.8203\,u$$ 4. **Mass defect** $$\Delta m = m_{\text{initial}} - m_{\text{final}}$$ $$\Delta m = 235.0439 - 234.8203 = 0.2236\,u$$ 5. **Calculate Q-value** Using $$1\,u\,c^2 = 931\,\text{MeV}$$ So, $$Q = 0.2236 \times 931\,\text{MeV}$$ $$Q = 208.1716\,\text{MeV}$$ 6. **Final integer answer** $$Q \approx 208\,\text{MeV}$$ So the required integer answer is: $$\boxed{208}$$ 7. **Comparison with stored answer** Stored correct answer = $208$ This matches our derived result.

View written solutionFree

Correct answer: 208

\mathrm{U} \rightarrow \, ^{140}\mathrm{Ce} + \, ^{94}\mathrm{Zr} + n$$ The disintegration energy is $$Q = \left( m_{\text{initial}} - m_{\text{final}} \right)c^2$$ 2. **Initial mass** Given: $$m(^{235}\mathrm{U}) = 235.0439\,u$$ So, $$m_{\text{initial}} = 235.0439\,u$$ 3. **Final mass** Given: $$m(^{140}\mathrm{Ce}) = 139.9054\,u$$ $$m(^{94}\mathrm{Zr}) = 93.9063\,u$$ $$m(n) = 1.0086\,u$$ Hence, $$m_{\text{final}} = 139.9054 + 93.9063 + 1.0086$$ $$m_{\text{final}} = 234.8203\,u$$ 4. **Mass defect** $$\Delta m = m_{\text{initial}} - m_{\text{final}}$$ $$\Delta m = 235.0439 - 234.8203 = 0.2236\,u$$ 5. **Calculate Q-value** Using $$1\,u\,c^2 = 931\,\text{MeV}$$ So, $$Q = 0.2236 \times 931\,\text{MeV}$$ $$Q = 208.1716\,\text{MeV}$$ 6. **Final integer answer** $$Q \approx 208\,\text{MeV}$$ So the required integer answer is: $$\boxed{208}$$ 7. **Comparison with stored answer** Stored correct answer = $208$ This matches our derived result.