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JEE MAIN 2023
11-4-2023
Question
The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately: (Given mass of a nitrogen molecule $=4.6 \times 10^{-26} \mathrm{~kg}$ and take Boltzmann constant $\mathrm{kB}=1.4 \times 10^{-23} \mathrm{JK}^{-1}$ )
Select the correct option:
A
$523 \mathrm{~m} / \mathrm{s}$
B
$1260 \mathrm{~m} / \mathrm{s}$
C
$91 \mathrm{~m} / \mathrm{s}$
D
$27.4 \mathrm{~m} / \mathrm{s}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$V_{r m s}=\sqrt{\frac{3 k_B T}{m}}=\sqrt{\frac{3 \times 1.4 \times 10^{-23} \times 300}{4.6 \times 10^{-26}}}=523 \mathrm{~m} / \mathrm{s}$
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