Question

If three molecules have velocities 0.5, 1 and 2 km s–1 respectively, calculate
the ratio between their root mean square and average speeds.

Answer 1

it is given that, three molecules have velocities 0.5, 1 and 2 km/s respectively,

so, root mean square speed, Vrms = √[{(0.5)² + (1)² + (2)²}/3]

= √{(0.25 + 1 + 4)/3}

= √(1.75)

≈ 1.32287 km/s

and average speed, V = (0.5 + 1 + 2)/3

= (3.5)/3

= 1.1667 km/s

now we have to find ratio of root mean square and average speeds.

so, Vrms : V = 1.32287 : 1.1667

≈ 1.133856 : 1

≈ 1.13 : 1

hence, ratio of root mean square and average speeds is 1.13 : 1