Question

The respectively speeds of five molecules are $2,1,5,1.6,1.6$ and $1.2km/sec$. The most probable speed in $km/sec$ will be :

• A. $2$
• B. $1.58$
• C. $1.6$
• D. $1.31$

Answer 1

The correct option is D $1.31$

RMS velocity of gas molecules is calculated by -

$v_{rms}=\sqrt{\left[\right(2^2+{1.5}^2+{1.6}^2+{1.6}^2+{1.2}^2\left)/5\right]}$

$v_{rms}=\sqrt{12.8/5}$

$v_{rms}=1.6$ m/s

Most probable speed is calculated by -

$v_{mp}=\sqrt{2/3\times v_{rms}}$

$v_{mp}=0.816\times 1.6$

$v_{mp}=1.306\approx 1.31$ km/s

Therefore, the most probable speed of the gas is 1.31 km/s.

Hence, the correct option is $\text{D}$