Question

The respective speeds of five molecules are 2,1.5,1.6,1.6 and 1.2 km/sec. The most probable speed in km/sec will be
A. 2
B. 1.58
C. 1.6
D. 1.31

Answer 1

Correct Answer - D

Answer 2

RMS velocity of gas molecules is calculated by -

vrms​=√[(22+1.52+1.62+1.62+1.22)/5]​

vrms​=√12.8/5​

vrms​=1.6 m/s

Most probable speed is calculated by -

vmp​=√2/3×vrms​​

vmp​=0.816×1.6

vmp​=1.306≈1.31 km/s

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

Hence, the correct option is D

Answer 3

Correct answer is (D)

Root mean square velocity = \(\sqrt{\frac{2 + 1.5 + 1.6 + 1.6 + 1.2}{5}}\)

V_rms = \(\sqrt{1.58}\)

We know that relation b/w most probable speed and root mean square velocities

V_most = \(\sqrt{\frac{2}{3}}\) V_rms

V_most = \(\sqrt{\frac{2}{3}}\) × \(\sqrt{1.58}\)

V_most = \(\sqrt{1.05}\)

V_most = 1.024 km/s