question_answer

BE/nucleon relation with mass number

A)  first decreases then increases

B)  first increases then decreases

C)  increases

D)  decreases

Correct Answer: B

Solution :

 Key Idea : The binding energy per nucleon for light nuclei is very small. The variation of average binding energy y per nucleon with mass number A is shown in figure. Average binding energy per nucleon for light nuclei like \[_{1}{{H}^{1}},{{\,}_{1}}{{H}^{2}},{{\,}_{1}}{{H}^{3}}\] is small. For mass numbers ranging from 2 to 20, there are sharply defined peaks corresponding to \[_{2}H{{e}^{4}},{{\,}_{6}}{{C}^{12}},{{\,}_{8}}{{O}^{16}}\] etc. The binding energy curve has a broad maximum in the range \[A=30\] to \[A=120\] corresponding to average binding energy per nucleon = 8.5 MeV. The peak value of the maximum is 8.8 MeV/nucleon for\[_{26}F{{e}^{56}}\]. As the mass number increases, the binding energy per nucleon decreases gradually falling to about 7.6 MeV per nucleon for \[_{92}{{U}^{238}}\].