A flask contains argon and oxygen in the ratio of $$3 : 2$$ in mass and the mixture is kept at $$27°$$C. The ratio of their average kinetic energy per molecule respectively

We need to find the ratio of average kinetic energy per molecule for argon and oxygen at the same temperature.

Argon (Ar) is a monoatomic gas with degrees of freedom $$f_1 = 3$$

Oxygen (O$$_2$$) is a diatomic gas with degrees of freedom $$f_2 = 5$$

The average kinetic energy per molecule of a gas is given by:

$$E = \frac{f}{2}k_BT$$

where $$f$$ is the number of degrees of freedom, $$k_B$$ is Boltzmann's constant, and $$T$$ is the temperature.

Since both gases are at the same temperature ($$27°$$C = 300 K):

$$\frac{E_{Ar}}{E_{O_2}} = \frac{\frac{f_1}{2}k_BT}{\frac{f_2}{2}k_BT} = \frac{f_1}{f_2} = \frac{3}{5}$$

Note: The mass ratio (3:2) is irrelevant here as the average kinetic energy per molecule depends only on degrees of freedom and temperature, not on the total mass of the gas.

Hence, the correct answer is Option A.