A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is [2021

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Solution

Q.
A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is [2021]

1 216 MeV

2 0.9 MeV

3 9.4 MeV

4 804 MeV

Ans.
(1)

Let the parent nucleus be $X$ which breaks into two fragments $Y$

${}^{240}X \to 2^{120} Y$

Binding energy of $X$ , ${B.E.}_{X} = 240 \times 7.6 = 1824$ MeV

Binding energy of $Y$ , ${B.E.}_{Y} = 120 \times 8.5 = 1020$ MeV

Energy released, $E = 2 {(B.E.)}_{Y} - {(B.E.)}_{X}$

$= 2 \times (1020) - 1824 = 216$ $MeV$

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