Question

If three molecules of oxygen at 27°C have velocities 0.5 km/s, 1 km/s and 2 km/s respectively. Then their root mean square speed will be
A) 1.7 km/s
B) 1.32 km/s
C) 1.13 km/s
D) 1.17 km/s​

Answer 1

Explanation:

(Vrms)^2=V1^2+V2^2+V3^2 / 3

(Vrms)^2=0.25+1+4/3

(Vrms)^2=1.75

Vrms=1.323 km/s

Answer 2

Given:

Three molecules of oxygen at 27°C have velocities 0.5 km/s, 1 km/s and 2 km/s respectively.

To find:

RMS speed ?

Calculation:

• Let RMS speed be v_(RMS)

$\rm \: v_{RMS} = \sqrt{ \dfrac{ {(v_{1})}^{2} + {(v_{2})}^{2} + {(v_{3})}^{2}}{3} }$

$\rm \implies\: v_{RMS} = \sqrt{ \dfrac{{(0.5)}^{2} + {(1)}^{2} + {(2)}^{2}}{3} }$

$\rm \implies\: v_{RMS} = \sqrt{ \dfrac{0.25 + 1 + 4}{3} }$

$\rm \implies\: v_{RMS} = \sqrt{ \dfrac{5.25}{3} }$

$\rm \implies\: v_{RMS} = \sqrt{ 1.75 }$

$\rm \implies\: v_{RMS} = 1.32 \: km/s$

So RMS velocity is 1.32 km/s.