At 300 K, the rms speed of oxygen molecules is √(α+5α) times to that of its average speed in the gas. Then, the value of α will be (use π=22/7)

Correct answer: (B) 28. RMS speed is given by, v_rms=√3RTM and average speed is given by, v_avg=√(8πRTM). As per question, v_rms=√(α+5α)v_avg ⇒√3RTM=√(α+5α)√(8πRTM) ⇒3=(α+5)/(α)×8/227 ⇒α=28

Q75 / 90 · JEE Main 2023 (29 Jan Shift 2) · Physics

At $300 K$ , the rms speed of oxygen molecules is $\sqrt{\frac{α + 5}{α}}$ times to that of its average speed in the gas. Then, the value of $α$ will be (use $π = \frac{22}{7}$ )

A
$32$
Correct answer
B
$28$
C
$24$
D
$27$

Solution

RMS speed is given by, $v_{r m s} = \sqrt{\frac{3 R T}{M}}$ and average speed is given by, $v_{a v g} = \sqrt{\frac{8}{π} \frac{R T}{M}}$ .

As per question,

$v_{r m s} = \sqrt{\frac{α + 5}{α}} v_{a v g}$

$\Rightarrow \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{α + 5}{α}} \sqrt{\frac{8}{π} \frac{R T}{M}}$

$\Rightarrow 3 = \frac{α + 5}{α} \times \frac{8}{\frac{22}{7}}$

$\Rightarrow α = 28$

Hence, the correct answer is option: 'B'.

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At 300 K, the rms speed of oxygen molecules is α+5α times to that of its average speed in the gas. Then, the value of α will be (use π=227)

Solution

Relevant Questions

At $300 K$ , the rms speed of oxygen molecules is $\sqrt{\frac{α + 5}{α}}$ times to that of its average speed in the gas. Then, the value of $α$ will be (use $π = \frac{22}{7}$ )