Question

Mass of proton =1.00760amu, mass of neutron =1.00899amu, mass of deuterium nucleus = 2.0147amu. Then binding energy is.

\[\begin{align}
  & A.\text{ }0.00189MeV. \\
 & \text{B}\text{. }1.76amu. \\
 & \text{C}\text{. }1.76MeV. \\
 & \text{D}\text{. }{{10}^{15}}joules. \\
\end{align}\]

Answer 1

Hint: We will need to use Albert Einstein’s relativity equation $E=m{{c}^{2}}$where E (also written as B.E) is binding energy, m is the mass defect, and c is the speed of light (in this case it is squared). The mass defect is the difference between the sum of the mass of all the individual nucleons that make up the nucleus, and the nucleus itself.

Formula used:
Velocity of transverse wave in a stretched string is,
$E=\Delta m{{c}^{2}}$
$\Delta m=\left[ Z{{m}_{p}}+\left( A-Z \right){{m}_{n}}+{{m}_{N}} \right]$

Complete step by step answer:
${}_{1}^{2}H\to 1proton+1neutron$
We will firstly calculate mass defect
The formula for mass defect is
$\begin{align}
  & \Delta m=\left[ Z{{m}_{p}}+\left( A-Z \right){{m}_{n}}+{{m}_{N}} \right] \\
 & \Delta m=\left[ 1.0076+1.00899+2.0147 \right] \\
 & \Delta m=0.00189\mu \\
\end{align}$
Now we will calculate the binding energy using the formula
$\begin{align}
  & E=\Delta m{{c}^{2}} \\
 & B.E=0.00189\times 931.478MeV \\
 & B.E=1.76MeV \\
\end{align}$
Hence the binding energy is $1.76MeV$.
Therefore the correct option is C.

Additional information:
Nuclear separation energy derives from the nuclear force or residual strong interaction, which is mediated by three sorts of mesons. The typical nuclear separation energy per nucleon ranges from 2.22452 MeV for hydrogen-2 to eight .7945 MeV for nickel-62.
Nuclear separation energy also can be considered the quantity of energy needed to stay the nucleons together, especially against the repulsive Coulomb force acting between protons

Note:
We know that at the nuclear level, nuclear separation energy is that the energy required to disassemble a nucleus into the free, or unbound neutrons and protons. It is the energy equivalent of the mass deficiency, the difference between the nucleon number of a nucleus and its true measured mass. Nucleons attract each other. This counteracts the repulsive force between the positively charged protons. The binding energy is the energy that is needed to split the atomic nucleus in its constituting nucleons (protons and neutrons; in case of antimatter: antiprotons and antineutrons). Hence, binding energy is negative, except in the case of hydrogen-1, in which it is zero (hydrogen-1 has only one proton in its nucleus. So there is no nuclear bond).