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 J K⁻¹]

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(3) 15 mm s⁻¹. A smoke particle in Brownian motion shares the thermal energy of the air, so the same formula applies. vᵣₘₛ=√(3k_BT)/m with T=273 K at NTP. 3k_BT=3×1.38×10⁻²³×273=1.13×10⁻²⁰. (3k_BT)/m=(1.13×10⁻²⁰)/(5×10⁻¹⁷)=2.26×10⁻⁴. vᵣₘₛ=√2.26×10⁻⁴=1.5×10⁻² m/s=15 mm/s.

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 J K⁻¹]

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