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Question:

The binding energy per nucleon of ⁷Li and ⁴He are 5.60 MeV and 7.06 MeV, respectively. In the nuclear reaction ⁷Li + ¹H → ⁴He + ⁴He + Q, the value of energy Q released is?

-6.4 MeV

19.6 MeV

8.4 MeV

17.3 MeV

Solution:

The binding energy of ⁷Li is 7 nucleons * 5.60 MeV/nucleon = 39.2 MeV.
The total binding energy of two ⁴He nuclei is 2 * (4 nucleons * 7.06 MeV/nucleon) = 56.48 MeV.
The energy released Q is the difference in binding energies:
Q = (total binding energy of products) - (total binding energy of reactants)
Q = 56.48 MeV - 39.2 MeV = 17.28 MeV
Therefore, the value of energy Q released is approximately 17.3 MeV.