Q79 / 90 · JEE Main 2022 (29 Jul Shift 2) · Physics

The root mean square speed of smoke particles of mass 5×10-17 kg in their Brownian motion in air at NTP is approximately.

[Given k=1.38×10-23J K-1]

  • A
    60 mm s-1
  • B
    12 mm s-1
  • Correct answer
    C
    15 mm s-1
  • D
    36 mm s-1

Solution

According to Kinetic theory, 

Average kinetic energy of a gas molecule =12mvrms2=32kT

Thus, vrms=3kTm

At NTP, T=293 K

Putting the values, we have

=3×1.38×10-23×2935×10-17

≈15 mm s-1

Hence, the correct answer is option: 'C'.

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