Question

What is the binding energy per nucleon of $C_6^{12}$ nucleus from the following data:
Given, Isotropic mass of $C_6^{12}$ \[ = 12.000\]u, $1u = 931MeV$
Mass of proton (${m_p}$) \[ = 1.00758\]u
Mass of neutron (${m_n}$) $ = 1.00893$u
Mass of electron (${m_e}$)\[ = {\text{ }}0.0055\]u
and \[1{\text{ }}amu\]\[ = 931.4{\text{ }}MeV\]
A) $7.94MeV$
B) $6.34MeV$
C) $8.84MeV$
D) none of the above

Answer 1

Hint: Nuclear binding energy accounts for an obvious difference between the particular mass of an atom’s nucleus and its expected mass supporting the sum of the masses of its non-bound components.

Complete step by step answer:
The actual mass is often but the sum of the individual masses of the constituent protons and neutrons because energy is removed when the nucleus is made. This energy has mass, which is faraway from the whole mass of the initial particles. This mass, referred to as the mass deficiency, is missing within the resulting nucleus and represents the energy released when the nucleus is created.
Mass defect (Md) are often calculated because the difference between observed mass (om) which expected from the combined masses of its protons
Step by step solution
\[
  \begin{array}{*{20}{l}}
  {\Delta m = \left[ {N \times M\left( p \right) + N \times M(n) - M\left( c \right)} \right]} \\
  { = \left[ {(6 \times 1.00758 + 6 \times 1.00893) - 12} \right]}
\end{array} \\
   = 0.09906u \\
\]

Once a mass defect is known, nuclear binding energy will be calculated by converting that mass to energy by using\[E = m{c^2}\]. Mass should be in units of kg.

As \[1u\] corresponds to \[931.494MeV\;/{c^2}\]energy, therefore, mass defect is equal to to the energy
Binding energy (${E_b}$)$ = \Delta m{c^2}$, substituting the value of u in the equation below we get:
\[
  Eb = 0.09906{c^2} \times 931.5MeV/{c^2} \\
   = 92.2743MeV \\
\]
Binding energy per nucleon is equal to$ = $binding energy$/$number of nucleons
Number of nucleon is equal to $ = $number of protons$ + $number of neutrons
$= 6 + 6 = 12 $

So Binding energy per nucleon will be as follows:
$
   = \dfrac{92.2743}{12} \\
   = 7.6895MeV \\
 $

So, the correct answer is Option D.

Note: Nuclear separation energy is that the energy required to separate a nucleus of an atom into its parts: protons and neutrons, or, collectively called, the nucleons. The energy of nuclei is usually a positive number because all nuclei require net energy to separate them into individual protons and neutrons.
Nuclear energy also can be applicable to situations when the nucleus splits into fragments composed of over one nucleon, in such cases, the binding energies for the fragments, as compared to the entire, are either positive or negative, reckoning on where the parent nucleus and also the daughter fragments fall on the nuclear separation energy curve.