91Ó°ÊÓ

The formula for the rms speed (\(v_{rms}\)) of a gas molecule is given by the following equation: $$v_{rms} = \sqrt{\frac{3 R T}{M}}$$ Here, - \(v_{rms}\) is the rms speed of the gas molecule - \(R\) is the gas constant - \(T\) is the temperature in Kelvin - \(M\) is the molar mass of the gas

Now, compare the rms speed formula with each of the given options: - Option (A): \(\sqrt{(M / 3 R T)}\) – This is not the correct formula, as it has \(M\) in the numerator and \(3 R T\) in the denominator, which is the opposite of the correct formula. - Option (B): \((M / 3 R T)\) – This is not the correct formula, as the numerator and denominator are reversed compared to the correct formula, and there is no square root. - Option (C): \(\sqrt{(3 R T / M)}\) – This is the correct formula, as it has the correct numerator and denominator in the square root. - Option (D): \((3 R T / M)^{2}\) – This is not the correct formula, as it has the correct numerator and denominator but raises the expression to the power of 2 instead of taking the square root.

Based on the comparison in step 2, Option (C) \(\sqrt{(3 R T / M)}\) is the correct formula for the rms speed of a gas molecule.