Question

The rms speed of hydrogen molecules at any temperature is 1996 m/s. The rms speed of colloidal particles with gram molecular weight $32\times {10}^{5}gmo{l}^{-1}$ will be

• A. $5.40m{s}^{-1}$
• B. $4.99m{s}^{-1}$
• C. $2.70m{s}^{-1}$
• D. $1.57m{s}^{-1}$

Answer 1

The correct option is D $1.57m{s}^{-1}$

RMS velocity is inversely proportional to the square root of molecular weights of the particles.

$\therefore$ $V\propto \sqrt{\frac{1}{M}}$

Thus we get $\frac{V_{particle}}{V_{Hydrogen}}=\sqrt{\frac{M_{Hydrogen}}{M_{particle}}}$

Molecular weight of hydrogen $M_{Hydrogen}=2gmo{l}^{-1}$

Molecular weight of colloidal particle $M_{particle}=32\times {10}^{5}gmo{l}^{-1}$

$\therefore$ $\frac{V_{particle}}{1996}=\sqrt{\frac{2}{32\times {10}^5}}$

$⟹$ $V_{particle}=1.57m/s$