A. Calculate (in MeV) the binding energy per nucleon for
12C.
B. Calculate (in MeV) the binding energy per nucleon for
13C.
C. Which is more tightly bound?
Answer
The binding energy is given as, my 1.00783u m1.00866u mc 13.00336u The binding energy for C wil thus be, 6(1.00783 )7(1.00866 u)-13.00336 u 0.10424 ux 97.099 MeV 931.49 MeV The binding energy per nucleon will be, 97.099 Mev 13 7.47 MeV The binding energy for C will thus be 6(1.00783 u)+6(1.00866 u)-12 u 0.09894 ux 92.162 MeV 931.49 MeV The binding energy per nucleon will be, 92.162 Mev 12 7.68 MeV Since the Binding energy of C is more than the binding energy of C atom, hence the C is more tightly bound.
The mass of proton is given as follows m, 1.00727647 amu The mass of neutron is given as follows: m,1.008664 amu follows The mass of C-12 is given as mc-12=12 amu The mass of C-13 is given as follows mc-13 13.00335 amu A. The binding energy per nucleon of C-12 is given as follows: S p(m,)+n(m,)-mc-12 BE 6+6 )- 12 6(1.00727647 amu )+6 (1.008664 amu 931.5 MeV amu 6+6 1 amu 7.424 MeV/nucleon B. The binding energy per nucleon of C-13 is given as follows: P(m,)+n(m)-mc-13 BE 6+7 np 6 1.00727647 amu )+7 (1.008664 amu )-13 931.5 MeV amu 6+7 1 amu 7.234 MeV/nucleon C. The binding energy per nucleon is greater for C-12 that C-13. Therefore, C-12 is more tightly bound.