Question

What is the binding energy of Nitrogen?

Answer 1

Hint: The binding energy can be defined as the amount of energy required to disassemble a system of particles into individual parts. It is equal to the mass defect; mass defect can be calculated from the sum of the mass of the protons and neutrons and the mass of the nucleus.
Formula Used:
\[\Delta m = \left( {7{m_p} + 7{m_n}} \right) - m\]
\[\Delta m\] is binding energy
\[{m_p}\] is mass of proton
\[{m_n}\] is mass of neutron
\[m\] is the mass of nucleus

Complete answer:
Proton is a positively charged subatomic particle having the mass of \[1.00783\] amu
Neutron is a no charged subatomic particle having the mass of \[1.00867\] amu
The given atom is Nitrogen, it has seven protons and seven neutrons.
Nitrogen is a nucleus containing \[7\] protons and \[7\] neutrons.
The number of electrons and the number of protons in a nucleus are the same, and leads to the stability of an atom.
That atomic mass of a given nitrogen atom is \[14.0037\] amu
The mass defect can be calculated as follows:
\[\Delta m = \left( {7{m_p} + 7{m_n}} \right) - m\]
Substitute the values in the above equation,
\[\Delta m = \left( {7 \times 1.00783 + 7 \times 1.00867} \right) - 14.0037\]
We will get,
\[\Delta m = 0.1124\] amu
Thus, the calculated mass defect is \[0.1124\] amu
To convert the binding energy in atomic mass unit to MeV the value should be multiplied with \[931MeV\]
Thus, the binding energy will be
\[\Delta m \times 931MeV\]
Substitute the obtained mass defect in the above equation,
\[0.1124 \times 931MeV = 104.67MeV\]
Thus, the binding energy will be \[104.67MeV\]
Thus, the binding energy of nitrogen is \[104.67MeV\]

Note:
The binding energy is the same as the mass defect, and can be determined from the mass of the nucleus and mass of proton and mass of neutron. The atomic mass unit (amu) and MeV are the units of binding energy.