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The binding energies per nucleon for deu...

The binding energies per nucleon for deuterium and helium are `1.1 MeV` and `7.0 MeV` respectively. What energy in joules will be liberated when `2` deuterons take part in the reaction.

Text Solution

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`"" _(1) ^(2)H+""_(1) ^(2) H to "" _(2) ^(4) He + Q`
Binding energy per nucleon of helium `(""_(2) ^(4) He)= 7 MeV`
Binding energy `= 4 x 7 = 28 MeV`
Binding energy per nucleon of deuterium `(""_(1) ^(2) H ) =1.1 MeV`
Binding energy `= 2x 1.1 =2.2 MeV`
Energy liberated `(Q) = (28-(2.2)2] = 23. 6 `Mev. i.e.,
`Q = 23. 6x 10 ^(6) x 1.6 xx 10 ^(-19) , Q = 37.76 xx 10 ^(-13)J`
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