Modern Physics Ques 211
- Consider the nuclear fission process
$Ne^{20} \rightarrow 2 He^{4}+C^{12}$
Given that the binding energy per nucleon of $Ne^{20}, He^{4}$ and $C^{12}$ are respectively, $8.03$ $ MeV, 7.07 $ $MeV$ and $7.86 $ $MeV$, identify the correct statement.
(Main 2019, 10 Jan II)
(a) Energy of $3.6 $ $MeV$ will be released.
(b) Energy of $12.4 $ $MeV$ will be supplied.
(c) $8.3\ \text{MeV}$ energy will be released.
(d) Energy of $11.9 $ $MeV$ has to be supplied.
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Answer:
Correct Answer: 211.(*)
Solution:
Formula:
- Energy absorbed or released in a nuclear reaction is given by
$\Delta Q=$ Binding energy of reactants - Binding energy of products.
If energy is absorbed, $\Delta Q$ is positive and if it is negative then energy is released.
Also, Binding energy $=$ Binding energy per nucleon $\times$ Number of nucleons.
Here, binding energy of the products
$ \begin{aligned} & =2 \times\left(\text { B.E. of } He^{4}\right)+\left(\text { B.E. of } C^{12}\right) \\ & =2(4 \times 7.07)+(12 \times 7.86)=150.88 MeV \end{aligned} $
and binding energy of reactants $=20 \times 8.03=160.6 $ $MeV$
So,
$\begin{aligned} \Delta Q= & (\text { B.E. }) _{\text {Products }}-(\text { B.E. }) _{\text {reactants }} \\ & =150.88-160.6=-9.72 MeV\end{aligned}$
As $\Delta Q$ is negative.
$\therefore$ energy of $9.72$ $MeV$ is absorbed in the reaction.
$\therefore$ No option is correct
BETA
