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

Question

The rms speed of particle of mass 5 × 10-17 kg. in their random motion in air at NTP will be (Boltzmann's constant) K =1.38 × 10-23 J / K (A) 15 × 10 m / s (B) 15 × 10-3 m / s (C) 10 × 10-2 m / s (D) 1.5 × 102 m / s

Tardigrade Admin · Accepted Answer

Given Mass of the particle m=5 × 10-17 kg Absolute temperature =273 K The rms speed of the particle is given by v rms =√(3 K T/m)=√(3 × 1.38 × 10-23 × 273/5 × 10-17) =√226 × 10-6=15 × 10-3

Q. The rms speed of particle of mass $5 \times 1 0^{- 17} k g$ . in their random motion in air at NTP will be (Boltzmann's constant) $K = 1.38 \times 1 0^{- 23} J / K$

$15 \times 10 m / s$

$15 \times 1 0^{- 3} m / s$

$10 \times 1 0^{- 2} m / s$

$1.5 \times 1 0^{2} m / s$

Given
Mass of the particle $m = 5 \times 1 0^{- 17} k g$
Absolute temperature $= 273 K$
The rms speed of the particle is given by
$v_{r m s} = \frac{3 K T}{m} = \frac{3 \times 1.38 \times 1 0 ^{- 23} \times 273}{5 \times 1 0 ^{- 17}}$
$= 226 \times 1 0^{- 6} = 15 \times 1 0^{- 3}$

Q. The rms speed of particle of mass 5×10−17kg. in their random motion in air at NTP will be (Boltzmann's constant) K=1.38×10−23J/K

15×10m/s

15×10−3m/s

10×10−2m/s

1.5×102m/s