States of Matter - Result Question 12
12. For gaseous state, if most probable speed is denoted by $C^{*}$, average speed by $\bar{C}$ and root mean square speed by $C$, then for a large number of molecules, the ratios of these speeds are
(2013 Main)
(a) $C^{*}: \bar{C}: C=1.225: 1.128: 1$
(b) $C^{*}: \bar{C}: C=1.128: 1.225: 1$
(c) $C^{*}: \bar{C}: C=1: 1.128: 1.225$
(d) $C^{*}: \bar{C}: C=1: 1.225: 1.128$
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Answer:
Correct Answer: 12. (c)
Solution:
$C^{*}=$ Most probable speed $=\sqrt{\dfrac{2 R T}{M}}$
$ \bar{C}=\text { Average speed }=\sqrt{\dfrac{8 R T}{\pi M}} $
$C=$ Root mean square speed
i.e.
rms $=\sqrt{\dfrac{3 R T}{M}}$ and as we know $\dot {\hat{C}} <\bar {C} < C $
$ \stackrel{*}{C}: \bar{C}: C=1: \sqrt{\dfrac{4}{p}}: \sqrt{\dfrac{3}{2}}=1: 1.128: 1.225 $
BETA
