Question

If the mass of proton=1.008a.m.u. and mass of neutron=1.009a.m.u., then binding energy per nucleon for $_4B{e^9}$ (mass=9.012amu) would be:
A. 40.065Mev
B. 60.44Mev
C. 67.2Mev
D. 6.72Mev

Answer 1

Hint: First we have to find a mass defect in a.m.u and binding energy of $_4B{e^9}$ in Mev and next we can calculate binding energy per nucleon in the unit of Mev. We have to know the rest mass of the stable nucleus of a stable atom is always less than the sum of the masses of constituent nucleons, so this difference is called the mass defect which is denoted by Δm.

Complete answer:
Binding energy is nothing but is the energy which is used in keeping the nucleons bound together. If the mass of a nucleus is always less than the mass of constituent (protons and neutrons) nucleons. This mass difference is called a mass defect and is denoted as Δm.
The general formula of finding mass defect is.
Δm = Z. mp + (A – Z). mn – M (Z, A)
Where mn is the mass of a neutron.
Mp is the mass of a proton.
M (Z, A) is the mass of bounded nucleus
Z is the atomic number
A is the atomic mass number.
According to question
$\begin{array}{l}
\Delta m = 4{m_p} + \left( {9 - 4} \right){m_n} - {m_{Be}}\\
 \Rightarrow \Delta m = \left( {4 \times 1.008 + 5 \times 1.009 - 9.012} \right)amu\\
\therefore 0.065amu
\end{array}$
Calculate Binding energy of $_4B{e^9}$
$\begin{array}{l}
 = \Delta m \times 931.5Mev\\
\end{array}$
Δm is the mass defect. Put this value in above equation
$\begin{array}{l}
 \Rightarrow 0.065 \times 931.5Mev\\
\therefore 60.5475Mev
\end{array}$
Now, we get the value of Binding energy of $_4B{e^9}$
But, binding energy per nucleon will be calculate as $\dfrac{{BE}}{{nucleon}}$
Put these value in above equation we get
$\begin{array}{l}
 \Rightarrow \dfrac{{60.5475}}{9}\\
\therefore = 6.7275Mev
\end{array}$

Hence the given option D is the correct answer.

Note:
There is a special case to know Einstein's law of inter-conversion of mass into energy where mass-defect is in the form of energy and is responsible for binding the protons and neutrons together to form a nucleus. We can study with the help of binding energy per nucleon curve with mass number.