Question

In a gas, $10$% molecules have a velocity of $2km/sec$ and $8$% molecules have a velocity of $1.5km/sec$ and $82$% molecules have a velocity $1km$. per sec. The most probable velocity of molecules is

• A. $1km/sec.$
• B. $1.5km/sec.$
• C. $2km/sec.$
• D. $15km/sec.$

Answer 1

Answer: (A)

$1km/sec.$

$V_{avg}=\frac{10\times 2+8\times 1.5+82\times 1}{100}=1.14$

$V_{avg}=\sqrt{\frac{8RT}{\pi M}}$ and $V_{MP}=\sqrt{\frac{2RT}{M}}$

$\therefore \frac{V_{avg}}{V_{MP}}=\frac{2}{\sqrt{\pi }}$

$\therefore V_{MP}=\frac{\sqrt{\pi }}{2}\times V_{avg}=1$ $km/sec$