Question

The $RMS$ velocity of a gas is $3.5$ $\times$ 10${}^4$ $cm/sec$.

The most probable velocity of the molecules is:

• A. $2.856$ $\times$ 10${}^4$ $cm/sec$
• B. $3.22$ $\times$ 10${}^4$ $cm/sec$
• C. $3.798$ $\times$ 10${}^4$ $cm/sec$
• D. $4.289$ $\times$ 10${}^4$ $cm/sec$

Answer 1

The correct option is A $2.856$ $\times$ 10${}^4$ $cm/sec$

The RMS velocity of the gas is = $3.5\times {10}^4$ cm/sec

Most probable velocity = $\sqrt{\frac{2RT}{M}}$

$\sqrt{\frac{3RT}{M}}=3.5\times {10}^4⟹\sqrt{\frac{RT}{M}}=\frac{3.5\times {10}^4}{\sqrt{3}}=2.02\times {10}^4\sqrt{\frac{2RT}{M}}=\sqrt{2}\times 2.02\times {10}^4{U}_{MPS}=2.856\times {10}^{4}cm/sec$