States of Matter - Result Question 17
17. For a monatomic gas kinetic energy $=E$. The relation with rms velocity is
(a) $u=\left(\dfrac{2 E}{m}\right)^{1 / 2}$
(b) $u=\left(\dfrac{3 E}{2 m}\right)^{1 / 2}$
(c) $u=\left(\dfrac{E}{2 m}\right)^{1 / 2}$
(d) $u=\left(\dfrac{E}{3 m}\right)^{1 / 2}$
(2004, 1M)
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Answer:
Correct Answer: 17. (a)
Solution:
Kinetic energy $(E)=\dfrac{3}{2} k T$
$ \begin{aligned} \text { RMS speed }(u) & =\sqrt{\dfrac{3 k T}{m}} \\ \Rightarrow \quad u & =\sqrt{\dfrac{2 E}{m}} \end{aligned} $
BETA
