In a nuclear fusion reaction, two nuclei, A & B , fuse to produce a nucleus C , releasing an amount of energy `DeltaE` in the process. If the mass defects of the three nuclei are `DeltaM_A, DeltaM_B` & `DeltaM_C` respectively , then which of the following relations holds ? Here, c is the speed of light.

Options

A. `Delta M_(A) + Delta M_(B)= Delta M_(C) - Delta E//c^(2)`
B. `Delta M_(A) + Delta M_(B)= Delta M_(C) + Delta E//c^(2)`
C. `Delta M_(A)- Delta M_(B)= Delta M_(C) + Delta E//c^(2)`
D. `Delta M_(A) - Delta M_(B)= Delta M_(C) + Delta E//c^(2)`

Answer

A

Explanation

`A + B rarr C`
Energy released
`= ((E_(b))_(C)- [(E_(b))_(A) + (E_(b))_(B)]`
`= Delta M_(C) (c^(2)) - (Delta M_(A) + Delta M_(B))_(C^(2))`
`therefore Delta M_(A) + Delta M_(B)= Delta M_(C)- (Delta E)/(c^(2))`