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# At 400K the root mean square (rms) speed of a gas x (mol weight = 40) is equal to the most probable speed of gas Y at 60K. Find the molecular weight of gas Y

$(a)\;2\qquad(b)\;4\qquad(c)\;6\qquad(d)\;8$

$U_{rms} = U_{MP}$
$\Rightarrow \sqrt{\large\frac{3RT}{M_x}}= \sqrt{\large\frac{2RT}{M_y}}$
$\Rightarrow \sqrt{\large\frac{3R\times400}{40}}= \sqrt{\large\frac{2R\times60}{M_y}}$
$\Rightarrow M_y = 4$