The mean free path of molecules of a certain gas at STP is $$1500d$$, where $$d$$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $$373$$ K is approximately:

The mean free path is given by:

$$\lambda = \frac{k_BT}{\sqrt{2}\pi d^2 P}$$

At constant pressure, $$\lambda \propto T$$.

At STP (273 K): $$\lambda_1 = 1500d$$

At 373 K (same pressure):

$$\lambda_2 = \lambda_1 \times \frac{T_2}{T_1} = 1500d \times \frac{373}{273}$$

$$\lambda_2 = 1500d \times 1.366 \approx 2049d$$

This matches option 3: 2049d.

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