Verified Solution • 2025–26 Session moderate

QJEEM23Phe69b: JEE Main 2023 Physics - Class 11 JEEM23Phe69b Solution: At 300 K, the rms speed of oxygen molecules is times to that of …

At 300 K, the rms speed of oxygen molecules is α+5α\sqrt {{{\alpha + 5} \over \alpha }} times to that of its average speed in the gas. Then, the value of α\alpha will be

(used π=227\pi = {{22} \over 7} )

Multiple Choice Options

  • A 27
  • B 28
  • C 24
  • D 32

Step-by-Step Verified Solution

vrms=α+5αvavg{v_{rms}} = \sqrt {{{\alpha + 5} \over \alpha }} {v_{avg}}

3RTm=α+558RTπm\sqrt {{{3RT} \over m}} = \sqrt {{{\alpha + 5} \over 5}} \sqrt {{{8RT} \over {\pi m}}}

3×π8=α+5α{{3 \times \pi } \over 8} = {{\alpha + 5} \over \alpha }

3328=α+5α{{33} \over {28}} = {{\alpha + 5} \over \alpha }

α=28\alpha = 28

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