Answer
(a) $8.790MeV/nucleon$
(b) $7.570MeV/nucleon$
Work Step by Step
(a) First we find the mass of the protons and neutrons as:
$m_f=26(1.007825u)+30(1.008665u)=56.463400u$
Now, $\Delta m=m_f-m_i$
$\Delta m=56.463400u-55.934939u=0.528461u$
Now we can find the required energy
$E=\Delta mc^2$
We plug in the known values to obtain:
$E=0.528461u(\frac{931.5MeV/c^2}{1u})c^2$
$E=492.3MeV$
Now we can find the average binding energy per nucleon as
$\frac{E}{A}=\frac{492.3MeV}{56}=8.790MeV/nucleon$
(b) First we find the mass of the protons and neutrons as:
$m_f=92(1.007825u)+146(1.008665u)=239.984990u$
Now, $\Delta m=m_f-m_i$
$\Delta m=239.984990u-238.050786u=1.934204u$
Now we can find the required energy
$E=\Delta mc^2$
We plug in the known values to obtain:
$E=1.934204u(\frac{931.5MeV/c^2}{1u})c^2$
$E=1801.7MeV$
Now we can find the average binding energy per nucleon as
$\frac{E}{A}=\frac{1801.7MeV}{238}=7.570MeV/nucleon$
