Question

The energy required to separate the typical middle mass nucleus ${}_{50}{\text{Sn}}^{120}$ into its constituent nucleons.

Mass of ${}_{50}{\text{Sn}}^{120}\text{nucleus}=119.902199u$
Mass of proton $m_p=1.007825u$
Mass of neutron $m_n=1.008665u$

• A. $1212\text{MeV}$
• B. $1021\text{MeV}$
• C. $951\text{MeV}$
• D. $805\text{MeV}$

Answer 1

The correct option is B $1021\text{MeV}$

Binding energy is the energy required to separate a nucleus into constituent nucleons.

$\Rightarrow B.E=\Delta m{c}^2$

$\Rightarrow B.E=(Z{m}_p+(A-Z)m_n-M)\times c^2$

$\Rightarrow B.E=\left[\right(50\times 1.007825)+(120-50)1.008665-119.902199]\times u{c}^2$

We know that, $1u{c}^2=931.5\text{MeV}$

$\Rightarrow B.E=[50.39125+70.60655-119.902199]931.5\text{MeV}$

$\Rightarrow B.E=[1.095601\times 931.5\text{MeV}]$

$\Rightarrow B.E\approx 1021\text{MeV}$

Hence, option $\left(B\right)$ is correct.