To find the ratio of specific heats ($\gamma$) for a mixture, we use the values of molar heat capacities for monoatomic and diatomic gases.

1. Avogadro's Law: According to the sources, equal volumes of gases at the same temperature and pressure contain an equal number of moles ($n$) . Thus, we assume $n_1$ (monoatomic) = $n_2$ (diatomic) = 1 mole.
2. Molar Heat Capacities: From standard thermodynamic data :

• Monoatomic gas: $C_{v1} = \frac{3}{2}R$ and $C_{p1} = \frac{5}{2}R$.
• Diatomic gas: $C_{v2} = \frac{5}{2}R$ and $C_{p2} = \frac{7}{2}R$.

3. Heat Capacities of the Mixture: $C_{v,mix} = \frac{n_1C_{v1} + n_2C_{v2}}{n_1 + n_2} = \frac{1.5R + 2.5R}{2} = 2R$. $C_{p,mix} = \frac{n_1C_{p1} + n_2C_{p2}}{n_1 + n_2} = \frac{2.5R + 3.5R}{2} = 3R$.
4. Ratio (\gamma ): The ratio of specific heats of the mixture is $\gamma_{mix} = \frac{C_{p,mix}}{C_{v,mix}} = \frac{3R}{2R} = 1.5$.

This calculation aligns with Option D.