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The binding energies per nucleon for deu...

The binding energies per nucleon for deuteron `(""_(1)^(2)H)` and helium `(""_(2)^(4)He)` are 1.1 MeV and 7 MeV respectively. Determine the energy released when two deuterons fuse to form a helium nucleus `(""_(2)^(4)He)`.

Text Solution

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The fusion reaction is as under :
`""_(1)^(2)H+""_(1)^(2)Hto""_(2)^(4)He+Q` (energy)
Deuteron contains 2 nucleons. Binding energy per nucleon is 1.1 MeV. Binding energy of each deuteron nucleus is `2xx1.1` i.e. 2.2 MeV.
Total binding energy before reaction
= `2xx2.2` MeV = 4.4 MeV
Total binding energy after reaction
`4xx7` MeV = 28 MeV
Clearly the energy released is = (28 - 4.4) MeV
i.e. 23.6. MeV.
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