Question

What is the rms speed of a gas molecule of mass ${10}^{-12}$ gm at room temperature ${27}^o$ according to kinetic theory of gases?

• A. $0.35$ cm/sec
• B. $2.03\times {10}^2$ m/sec
• C. $0.70$ m/sec
• D. $0.35$ m/sec

Answer 1

The correct option is A $0.35$ cm/sec

According to the problem:

let m be the mass than $\frac{1}{2}m{u}^2$ is kinetic energy of this partical where, rms velocity

hence, the kinetic energy of molecule $=\frac{3RT}{2\times N}$

SINCE, $=\frac{1}{2}M{U}_2=\frac{3RT}{2N}$ $U=\sqrt{\left[3\frac{R}{N}\times \frac{T}{M}\right]}$

Given:

$m={10}^{-12}g$

$R=8.314\times {10}^{7}ergandt=300k$

$\Rightarrow$ that $=\sqrt{\frac{3\times 8.314\times {10}^7\times 300}{6.023\times {10}^{23}\times {10}^{-12}}}$

$u=0.35cm{\sec }^{-1}$