Because protons and neutrons are similar in mass, size, and certain other characteristics, a collective term, nucleons, has been coined that encompasses both of these constituents of the atomic nucleus. In many nuclei, nucleons are confined (by the strong force, discussed in Chapter$\mathbf{\text{11}}$) to dimensions of rough$\mathbf{\text{15}}$femtometers. Photons emitted by nuclei as the nucleons drop to lower energy levels are known as gamma particles. Their energies are typically in the Me$\mathbf{\text{V}}$range. Why does this make sense?

For the infinite well model, the energy of a particle is given by:

Where n is the number of energy levels.

$\hslash$is reduced Planck’s constant, $\hslash =h2\pi$ .

h is Planck’s constant ${\text{h=6.64×10}}^{\text{-34}}\text{J×s}$ .

m is the mass of an electron ${\text{=9.1×10}}^{\text{-31}}\text{kg}$ .

Lis the width of the quantum well.

Gamma rays are emitted when nucleons undergo a transition from a higher state to the lower state of the same nucleus.

The Gamma-ray energy spectrum shows discrete lines corresponding to each transition. The energies of gamma rays can vary from a few keV to many MeV equivalent to the characteristic energy levels in nuclei with practically long lifetimes. Any nucleus from hydrogen to element $\text{112}$can decay by gamma-ray emission.

Let the width of the infinite well be,${\text{L=1×10}}^{\text{-12}}\text{m}$

Assume that the gamma rays are emitted by the transition of nucleons from the state$\text{n=3}$ to the state$\text{n=2}$

Now substituting the numerical values in equation

$\begin{array}{c}\text{E=}\left(\text{32-22}\right)\left(\text{h2π}\right){\text{2π22×9.1×10}}^{\text{-31}}\left({\text{1×10}}^{\text{-12}}\right)\text{2}\\ {\text{E=3.02×10}}^{\text{-13}}{\text{J×6.24×10}}^{\text{18}}\text{eVJ.}\\ {\text{E=18.84×10}}^{\text{5}}\text{eV.}\\ \text{E=1.88MeV.}\end{array}$