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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 × 10⁻²³ JK⁻¹]
- 60 mm s⁻¹
- 12 mm s⁻¹
- 15 mm s⁻¹
- 36 mm s⁻¹
Correct answer: 15 mm s⁻¹
Solution
The root mean square speed of particles in Brownian motion can be calculated using the formula v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the particles. At normal temperature and pressure (NTP), the calculated speed for the given mass of smoke particles yields approximately 15 mm/s, confirming option C as the correct answer.
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