KCET · Physics · Nuclear Physics
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. \(\mathrm{B} \rightarrow 2 \mathrm{~A}\)
- A in (1), (2) and (3)
- B Only in (1)
- C in (2), (3)
- D in (1), (3)
Answer & Solution
Correct Answer
(B) Only in (1)
Step-by-step Solution
Detailed explanation
(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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