At what temperature in kelvin (nearest integer) is the root mean square speed of N2 (molar mass 28 g mol^-1) equal to 500 m s^-1? Take R = 8.314 J K^-1 mol^-1.

JEE Advanced levelNumerical answerDifficulty 3 of 3ig044

At what temperature in kelvin (nearest integer) is the root mean square speed of $N X_{2}$ (molar mass $28 g mo l^{- 1}$ ) equal to $500 m s^{- 1}$ ? Take $R = 8.314 J K^{- 1} mo l^{- 1}$ .

Numerical answer type, answer in K, tolerance 1.

u_{rms}^{2} = \frac{3 RT}{M}

, so

T = \frac{M u ^{2}}{3 R} = \frac{0.028 \times 50 0 ^{2}}{3 \times 8.314} = \frac{7000}{24.942} = 280.65 \approx 281 K