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NEET PHYSICSKinetic TheoryMedium

Question

The root-mean-square speed of hydrogen molecules at 300 K is 1930 m/s. Then the root mean square speed of oxygen molecules at 900 K will be:

A

1930√3 m/s

B

836 m/s

C

643 m/s

D

1930/√3 m/s

Step-by-Step Solution

The root mean square speed (vrmsv_{rms}) of gas molecules is given by the formula vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}}, implying vrmsTMv_{rms} \propto \sqrt{\frac{T}{M}} .

Given:

  1. Hydrogen (H2H_2): T1=300 KT_1 = 300 \text{ K}, v1=1930 m/sv_1 = 1930 \text{ m/s}. Molar mass M1=2 g/molM_1 = 2 \text{ g/mol} .
  2. Oxygen (O2O_2): T2=900 KT_2 = 900 \text{ K}. Molar mass M2=32 g/molM_2 = 32 \text{ g/mol} .

Calculation: vO2vH2=T2T1×M1M2\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{T_2}{T_1} \times \frac{M_1}{M_2}} vO21930=900300×232=3×116=34\frac{v_{O_2}}{1930} = \sqrt{\frac{900}{300} \times \frac{2}{32}} = \sqrt{3 \times \frac{1}{16}} = \frac{\sqrt{3}}{4} vO2=1930×1.7324836 m/sv_{O_2} = 1930 \times \frac{1.732}{4} \approx 836 \text{ m/s}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Kinetic Theory. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSKinetic Theoryrootmeansquarehydrogenmoleculessquareoxygen

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