The binding energy per nucleon of deuterium and helium nuclei are 1.1 MeV and 7.0 MeV respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

Options

A. 23.6 MeV
B. 2.2 MeV
C. 28.0 MeV
D. 30.2 MeV

Explanation

`""_(1)H^(2)+""_(1)H^(2)rarr""_(2)He^(4)+DeltaE`
The binding energy per nucleon of a deuteron = 1.1 MeV
`therefore" "` Total binding energy `=2xx1.1=2.2MeV`
The binding energy per nucleon of a helium nuclei = 7 MeV
`therefore" Total binding energy "=4xx7=28 MeV`
Hence, energy released
`DeltaE=(28-2xx2.2)=23.6MeV`