JEE MAIN - Physics (2023 - 29th January Evening Shift - No. 16)
At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average speed in the gas. Then, the value of $$\alpha$$ will be
(used $$\pi = {{22} \over 7}$$)
27
28
24
32
Explanation
$${v_{rms}} = \sqrt {{{\alpha + 5} \over \alpha }} {v_{avg}}$$
$$\sqrt {{{3RT} \over m}} = \sqrt {{{\alpha + 5} \over 5}} \sqrt {{{8RT} \over {\pi m}}} $$
$${{3 \times \pi } \over 8} = {{\alpha + 5} \over \alpha }$$
$${{33} \over {28}} = {{\alpha + 5} \over \alpha }$$
$$\alpha = 28$$
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