A nucleus with mass number 240 breaks into two fragments each of...

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 . 6MeV

while that of fragments is

8 . 5MeV

. The total gain in the binding energy in the process is : A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of

Options

A $0 . 9MeV$
B $9 . 4MeV$
C $216MeV$
D $804MeV$

Correct answer

C. $216MeV$

Step-by-step solution

Given binding energy per nucleon of $X, Y \text{ and } Z$ are, $7 . 6MeV, 8 . 5MeV \text{ and } 8 . 5MeV$ respectively.

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of

$⇒ B . E .$ $= ( 120 \times 8 . 5 ) + ( 120 \times 8 . 5 ) - 240 \times 7 . 6$

$⇒ B . E . = 2040 - 1824$ $= 216MeV$

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