The root mean square speed of smoke particles of mass 5 × 10-17kg in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 10-23 JK-1]

m = 5 × 10-17kg ; k = 1.38 × 10-23 Jk-1Vrms=3RTM=3NkTNm=3kTm=3×1.38×10−23×3005×10−17=18×13.8×10−6=15.7×10−3m/s=15mm/s

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The root mean square speed of smoke particles of mass 5 × 10^-17kg in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 10^-23 JK^-1]

Option 1 -

60 mm s^-1

Option 2 -

12 mm s^-1

Option 3 -

15 mm s^-1

Option 4 -

36 mm s^-1

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

m = 5 × 10^-17kg ; k = 1.38 × 10^-23 Jk^-1

$V_{r m s} = \sqrt[]{\frac{3 R T}{M}} = \sqrt[]{\frac{3 N k T}{N m}} = \sqrt[]{\frac{3 k T}{m}} = \sqrt[]{\frac{3 \times 1.38 \times 1 0^{- 23} \times 300}{5 \times 1 0^{- 17}}}$

$= \sqrt[]{18 \times 13.8 \times 1 0^{- 6}}$

$= 15.7 \times 1 0^{- 3} m / s$

$= 15 m m / s$

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