Question

The rms speed of particle of mass $5 \times 10^{-17} kg$. in their random motion in air at NTP will be (Boltzmann's constant) $K =1.38 \times 10^{-23} J / K$

• A. $15 \times 10 \,m / s$
• B. $15 \times 10^{-3} m / s$
• C. $10 \times 10^{-2} m / s$
• D. $1.5 \times 10^{2} m / s$

Answer 1

Answer: (B)

Given
Mass of the particle $m=5 \times 10^{-17} kg$
Absolute temperature $=273\, K$
The rms speed of the particle is given by
$v_{ rms } =\sqrt{\frac{3 K T}{m}}=\sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273}{5 \times 10^{-17}}}$
$=\sqrt{226 \times 10^{-6}}=15 \times 10^{-3}$