For gaseous state, if most probable speed is denoated by $C^{*}$, average speed by $\bar{C}$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

(B) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1: 1.128: 1.225$

(A) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.128: 1.225: 1$

(C) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1: 1.125: 1.128$

(D) $\mathrm{C}^{*}: \overline{\mathrm{C}}: \mathrm{C}=1.225: 1.128: 1$

JEE Main · 2013 · 07 Apr 2013 · Offline · States of Matter

For gaseous state, if most probable speed is denoated by

C^{*}

, average speed by

\overset{ˉ}{C}

and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

(A) $C^{*} : \overline{C} : C = 1.128 : 1.225 : 1$
(B) $C^{*} : \overline{C} : C = 1 : 1.128 : 1.225$ ✓ Correct
(C) $C^{*} : \overline{C} : C = 1 : 1.125 : 1.128$
(D) $C^{*} : \overline{C} : C = 1.225 : 1.128 : 1$

Answer: (B)

Solution

Kinetic theory fixes the three molecular speeds as the most probable

C^{*} = \frac{2 R T}{M}

, the average

\overset{ˉ}{C} = \frac{8 R T}{π M}

and the root-mean-square

C = \frac{3 R T}{M}

. Their ratio is

2 : 8/ π : 3

, which, normalised to the smallest, is

1 : 1.128 : 1.225

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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