The rms speed of oxygen molecule in a vessel at particular temperature is $$\left(1 + \frac{5}{x}\right)^{\frac{1}{2}}v$$, when $$v$$ is the average speed of the molecule. The value of $$x$$ will be:
(take $$\pi = \frac{22}{7}$$)

The rms speed and average speed of gas molecules are given by:

$$v_{rms} = \sqrt{\frac{3RT}{M}}, \quad v_{avg} = \sqrt{\frac{8RT}{\pi M}}$$

The ratio:

$$\frac{v_{rms}}{v_{avg}} = \sqrt{\frac{3RT/M}{8RT/(\pi M)}} = \sqrt{\frac{3\pi}{8}}$$

Given: $$v_{rms} = \left(1 + \frac{5}{x}\right)^{1/2} \cdot v_{avg}$$

Squaring both sides:

$$\frac{v_{rms}^2}{v_{avg}^2} = 1 + \frac{5}{x} = \frac{3\pi}{8}$$

$$\frac{5}{x} = \frac{3\pi}{8} - 1 = \frac{3\pi - 8}{8}$$

$$x = \frac{40}{3\pi - 8}$$

Using $$\pi = \frac{22}{7}$$:

$$3\pi - 8 = \frac{66}{7} - \frac{56}{7} = \frac{10}{7}$$

$$x = \frac{40}{\frac{10}{7}} = \frac{40 \times 7}{10} = 28$$

Therefore, the correct answer is Option C: $$\mathbf{28}$$.