Question

Four molecules of a gas have speeds $1,2,3$ and $4km{s}^{-1}$. The value of rms speed of the gas molecules is :

• A. $\frac{1}{2}\sqrt{15}km{s}^{-1}$
• B. $\frac{1}{2}\sqrt{10}km{s}^{-1}$
• C. $2.5km{s}^{-1}$
• D. $\frac{15}{2}km{s}^{-1}$

Answer 1

Answer: (D)

The square root of ${\bar{v}}^2$ is called the root mean square velocity (rms) speed of the molecules.
$v_{rms}=\sqrt{{\bar{v}}^2}$
$=\sqrt{\frac{v_1^2+v_2^2+v_3^2+v_4^2}{4}}$
$=\sqrt{\frac{(1{)}^2+(2{)}^2+(3{)}^2+(4{)}^2}{4}}$
$=\sqrt{\frac{1+4+9+16}{4}}$
$=\sqrt{\frac{30}{4}}$
$=\sqrt{\frac{15}{2}}km{s}^{-1}$