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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 rarr ._(2)^(4)He + Q`
Binding energy per nucleon of helium `(._(2)^(4)He) = 7 MeV`
Binding energy `= 4 xx 7 =28 Me V`
Binding energy nucleon of deuterium `(._(2)^(1)H) = 1.1 MeV`
Binding energy `= 2 xx 1.1 = 2.2 MeV`
Energy liberated `(Q) = (28 - (2.2)2] = 23.6 MeV`
i.e., `Q = 23.6 xx 10^(6) xx 6 xx 10^(-19), Q = 37.76 xx 10^(-13)J`
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