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# The RMS speed of the molecules of diatomic gas is U, when the temperature is doubled , the molecules dissociates into two atoms . The new RMS speed of the atom is

$(A)\;\sqrt2 U\qquad(B)\;U\qquad(C)\;2U\qquad(D)\;4U$

$U_{rms} = \sqrt{[\large\frac{3RT}{M}]}$
If T = 2T
$M = \large\frac{M}{2}$
then $U_1 = \sqrt{[\large\frac{3R\times 2T}{\large\frac{M}{2}}]}$
$\therefore \large\frac{U_1}{U} = \sqrt{4}$
$\;\;\;\;\;\;\;\;\;\;= 2$
edited Mar 24, 2014