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Let \mathrm{U_{a r}, U_{\text {mas }}} and \mathrm{U_{\text {mp }}} respectively denote the avenge spued, root mean square are age speed and most probable speed in on ideal monatomic g as at kelvin temperature. T. The mass of an atom is m. Then correct statements are-
(a) no atom can have a speed greaten than \mathrm{\sqrt{2} u_{rms}}.
(b) no atom can hare a speed greaten than \mathrm{u_{m p} / \sqrt{2}}
(c) \mathrm{ u_{\text {mp }}<u_{\text {av }}<u_{\text {rms }}}
(d) the average kinetic energy of an atom is \mathrm{ (3 / 4) m^2 mp}.

Option: 1

a and b only
 


Option: 2

c  and d only


Option: 3

b and d only 

 


Option: 4

 a, c and d only 


Answers (1)

best_answer

The expression of \mathrm{v_{a r}, v_{m m}}  and \mathrm{v_{m p}} are -

\mathrm{U_{a v}=\sqrt{\frac{8 R T}{\pi M}} ; U_{m m s}=\sqrt{\frac{3 R T}{M}} ; U_{m p}=\sqrt{\frac{2 R T}{M}} }

from these, it follows that,

\mathrm{ U_{m p}<U_{a v}<U_{r ms} }

The acreage kinetic energy of the gaseous atom is -

\mathrm{ \bar{E}=\frac{1}{2} m u_{r ms}^2=\frac{1}{2}\left(\frac{3}{2} u_{m p}^2\right)=\frac{3}{4} m u_{m p}^2 }
Option (c) and (d) are correct.

Posted by

vishal kumar

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