The nucleus of the deuterium atom, called the deuteron, consists of a proton and a neutron. Calculate the deuteron's binding energy, given atomic mass, i.e., the mass of a deuterium nucleus plus an electron is measured to be `2.014 102 u`.

Explanation

We know that the proton and neutron masses are
`m_(P) =1.007 825 u`, `m_(n) =1.008 665 u`
Note that tha masses used for the proton and neutron in this example are actually those of the neutral atoms. We are able to use atomic masses cancel out. That is, when `m_(d)` containing one electron mass is subtracted from `(m_(p) + m_(n))` containing one electron mass, the electron masses cancel out. We have,
`m_(p) + m_(n) =2.016 490 u`
To calculate the mass difference, we subtract the deuteron mass from this value.
`:. Dleta m =(m_(p) + m_(n)) -m_(d)`
` = 2.016 490 u - 2.014 102 u = 0.02 388 u `
Because `1 u` corresponds to an equivalent energy of `931 .494 MeV` , `(i.e., 1 u. c^(2) =931. 494 MeV)`, the mass difference corresponds to the binding energy
`E_(b) =(0.002 388 u) (931.494 MeV//u) =2.224 MeV`
This result tells us that to separate a deuteron into a proton and a neutron, it is necessary to add `2.224 MeV` of energy to the deuteron to overcome the attractive nuclear force between the proton and neutron. One way of supplying the deuteron with this energy is by bombarding it with energetic particles. If the binding energy of a nucleus were zero, the nucleus would separate into its constituent protons and neutrons without the addition of any energy, i.e., it would spontaneously break apart.