Question

Calculate the binding energy of a deutron atom, which consists of a proton and a neutron, given that the atomic mass of the deuteron is \[2.014102u\]
A.$0.00238MeV$
B.$2.014102MeV$
C.$2.16490MeV$
D.$2.224MeV$

Answer 1

Hint:
Nuclear binding energy accounts for a noticeable difference between the actual mass of an atom’s nucleus and its expected mass based on the sum of the masses of its non-bound components.
The actual mass is always less than the sum of the individual masses of the constituent protons and neutrons because energy is removed when the nucleus is formed. This energy has mass, which is removed from the total mass of the original particles. This mass, known as the mass defect, is missing in the resulting nucleus and represents the energy released when the nucleus is formed.
Mass defect (Md) can be calculated as the difference between observed atomic mass (mo) and that expected from the combined masses of its protons

Complete step by step answer:
Given
$M(D) = $\[2.014102u\]
atomic mass M(H) of hydrogen and nuclear mass (Mn​) are
\[M\left( H \right) = 1.007825u\;\]and \[M\left( n \right) = 1.008665u\]
\[
  \begin{array}{*{20}{l}}
  {\Delta m = \left[ {M\left( H \right) + M(n) - M\left( D \right)} \right]} \\
  { = 2.016490u - 2.014102u}
\end{array} \\
   = 0.002388u \\
\]

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


As \[1u\] corresponds to \[931.494MeV\;/{c^2}\]energy, therefore, mass defect corresponds to energy
Binding energy (${E_b}$)$ = \Delta m{c^2}$, substituting the value of u in the equation below
\[
  Eb = 0.002388{c^2} \times 931.5MeV/{c^2} \\
   = 2.224MeV \\
\]
So the correct answer is D)

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