Question

Calculate mass defect and binding energy per nucleon of ${ }_{10}^{20} \mathrm{Ne},$ given
Mass of ${ }_{10}^{20} \mathrm{Ne}=19.992397 \mathrm{u}$
Mass of ${ }_{1}^{1} \mathbf{H}=1.007825 u$
Mass of ${ }_{0}^{1} \mathbf{n}=1.008665 u .$

Answer 1

Hint: To decide whether fission or fusion would be a favorable operation, nuclear binding energy is used. The mass defect of the nucleus is the mass of the energy that connects the nucleus, which is the difference between the mass of the nucleus and the amount of the mass of the nucleons that make it up.
Formula used:
Mass defect $\Delta \mathrm{M}=10(\mathrm{~m})_{0}{ }_{0} \mathrm{n}+10(\mathrm{~m})_{1}{ }_{1} \mathrm{H}-(\mathrm{m})_{10}{ }_{20} \mathrm{Ne}$

Complete answer:
The energy required to break an atom's nucleus into its components is nuclear binding energy. The mass defect of the nucleus is the mass of the energy that connects the nucleus, which is the difference between the mass of the nucleus and the amount of the mass of the nucleons that make it up.
The required nuclear reaction is: $10_{0}^{1} \mathrm{n}+10{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{10}^{20} \mathrm{Ne}$
Mass defect $\Delta \mathrm{M}=10(\mathrm{~m})_{0}{ }_{0} \mathrm{n}+10(\mathrm{~m})_{1}{ }_{1} \mathrm{H}-(\mathrm{m})_{20}{ }_{0} \mathrm{Ne}$
$\therefore \Delta \text{M}=10(1.008665)+10(1.007825)-19.992397$
$\Rightarrow 0.172503\text{u}$
Binding energy of the nucleon
 $\mathrm{E}=\Delta \mathrm{M} \times 931.5 \mathrm{MeV}$
$\therefore \text{E}=0.172503\times 931.5$
$\Rightarrow 160.69\text{MeV}$
Binding energy per nucleon
 $\text{u}=\dfrac{\text{E}}{20}$
$\Rightarrow \dfrac{160.69}{20}$
$\Rightarrow 8.03\text{MeV}$
\[\therefore \]The mass defect and binding energy per nucleon of ${ }_{10}^{20} \mathrm{Ne},$ given by $\mathrm{u}=\dfrac{\mathrm{E}}{20}=\dfrac{160.69}{20}=8.03 \mathrm{MeV}$

Additional Information:
Once the mass defect is known, nuclear binding energy can be measured by using \[\text{E=m}{{\text{c}}^{2}}\] to turn the mass into energy. There must be mass in units of kg. It can be scaled into per-nucleon and per-mole quantities until this energy, which is a quantity of joules for one nucleus, is recognized. The mass defect of the nucleus is the quantity of mass equal to the binding energy of the nucleus, which is the difference between the mass of the nucleus and the sum of the individual masses of the nucleons that make it up.

Note:
The energy required to break the nucleus of an atom into protons and neutrons is nuclear binding energy. The disparity between the estimated mass and the real mass of the nucleus of an atom is a mass defect. A system's binding energy may appear as additional mass, which accounts for this difference.