The ratio of molar specific heat at constant pressure C_p, to molar specific heat at constant volume $C_V$ for monoatomic gas is

For monoatomic gas, the average energy of a molecule at temperature T= is $\frac{3}{2}{k}_{B}T$

Internal energy U = $\frac{3}{2}RT$

$$\begin{gathered} C_V= \frac{dU}{dT}=\frac{3}{2}R \\ For an ideal gas , C_P-C_V = R \\ {C}_P =\frac{5}{2}R and \gamma =\frac{C_P}{C_V}=\frac{5}{3} \end{gathered}$$