Question

A nuclear fusion reaction is given below:
${}_1{H}^2+{}_1{H}^2\to {}_{2}H{e}^3+n+3.2MeV$
How much energy will be generated when 2 kg of deutrons are fused: - (approx)

• A. ${10}^{30}eV$
• B. $5\times {10}^{23}MeV$
• C. ${10}^{22}MeV$
• D. ${10}^{33}eV$

Answer 1

Answer: (D)

${10}^{33}eV$

$Given:$ A nuclear fusion reaction is : ${}_1{H}^2+{}_1{H}^2\to {}_{2}H{e}^3+n+3.2MeV$

$Solution:$ For $2atoms$ of deutrons energy released $=3.2MeV$

$$\begin{array}{cc}2kg\text{deutrons}& =\frac{2\times {10}^3}{2}={10}^{3}moles\\ & ={10}^3\times N{}_A\text{atoms}\\ & =6.23\times {10}^{23}\times {10}^3\text{atoms}\\ 2\text{atoms}=& 3.2MeV\\ 1\text{atom}=& \frac{3.2}{2}MeV\\ \text{So,}6.23\times {10}^{23}& =\frac{3.2}{2}\times 6.23\times {10}^{26}Mev\\ & =9.968\times {10}^{26}\times {10}^{6}eV\\ & =9.968\times {10}^{32}eV\\ & \approx 10\times {10}^{32}eV\\ & \approx {10}^{33}eV\end{array}$$

$So,the$ $correct$ $option:D$