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

Question

At 300 K, the rms speed of oxygen molecules is √(α+5/α) times to that of its average speed in the gas. Then, the value of α will be (used π=(22/7) ) (A) 32 (B) 28 (C) 24 (D) 27

Tardigrade Admin · Accepted Answer

√(3 RT / M )=√(α+5/α) √(8/π) ( RT / M ) 3=(α+5/α) (8/π) α=28

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

32

28

24

27

$\frac{3 RT}{M} = \frac{α + 5}{α} \frac{8}{π} \frac{RT}{M}$
$3 = \frac{α + 5}{α} \frac{8}{π}$
$α = 28$

Q. At 300K, the rms speed of oxygen molecules is αα+5​​ times to that of its average speed in the gas. Then, the value of α will be (used π=722​ )

32

28

24

27

M3RT​​=αα+5​​π8​MRT​​ 3=αα+5​π8​ α=28

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

$\frac{3 RT}{M} = \frac{α + 5}{α} \frac{8}{π} \frac{RT}{M}$
$3 = \frac{α + 5}{α} \frac{8}{π}$
$α = 28$