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Mass number of the elements A, B, C and D are $30,60,90$ and 120 respectively. The specific binding energy of them are $5 \mathrm{MeV}, 8.5 \mathrm{MeV}$, $8 \mathrm{MeV}$ and $7 \mathrm{MeV}$ respectively. Then, in which of the following reaction/s energy is released?
1. $\mathrm{D} \rightarrow 2 \mathrm{~B}$
2. $\mathrm{C} \rightarrow \mathrm{B}+\mathrm{A}$
3. $\mathrm{B} \rightarrow 2 \mathrm{~A}$
Options:
1. $\mathrm{D} \rightarrow 2 \mathrm{~B}$
2. $\mathrm{C} \rightarrow \mathrm{B}+\mathrm{A}$
3. $\mathrm{B} \rightarrow 2 \mathrm{~A}$
Solution:
2721 Upvotes
Verified Answer
The correct answer is:
Only in (1)
(1) $\Delta \mathrm{E}=2 \times 60 \times 8.5-120 \times 7=180 \mathrm{MeV}$
(2) $\Delta \mathrm{E}=60 \times 8.5+30 \times 5-90 \times 8=-60 \mathrm{MeV}$
(3) $\Delta \mathrm{E}=2 \times 30 \times 5-60 \times 8.5=-105 \mathrm{MeV}$
Hence, energy is released in (1) only.
So, option (b) is correct.
(2) $\Delta \mathrm{E}=60 \times 8.5+30 \times 5-90 \times 8=-60 \mathrm{MeV}$
(3) $\Delta \mathrm{E}=2 \times 30 \times 5-60 \times 8.5=-105 \mathrm{MeV}$
Hence, energy is released in (1) only.
So, option (b) is correct.
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