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The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature, the rms speed of the oxygen molecules is vo. The rms speed of the hydrogen molecules at the same temperature will be
  • a)
    v0/16
  • b)
    v0/4
  • c)
    4v0
  • d)
    16v0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The mass of an oxygen molecule is about 16 times that of a hydrogen m...
Explanation:

The root mean square speed of a molecule is given by the formula:

v = √(3kT/m)

Where v is the root mean square speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the molecule.

Given that the mass of an oxygen molecule is 16 times that of a hydrogen molecule, we can write:

mO2 = 16mH2

Where mO2 is the mass of an oxygen molecule and mH2 is the mass of a hydrogen molecule.

Let's assume that the temperature is the same for both molecules. Therefore, we can write:

vO2 = √(3kT/mO2)

vH2 = √(3kT/mH2)

Substituting mO2 = 16mH2 in the equation for vO2, we get:

vO2 = √(3kT/16mH2)

Taking the ratio of vH2 and vO2, we get:

vH2/vO2 = √(3kT/mH2)/√(3kT/16mH2)

vH2/vO2 = √16

vH2/vO2 = 4

Therefore, the rms speed of the hydrogen molecules at the same temperature will be 4 times the rms speed of the oxygen molecules. Hence, the correct answer is option C.
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Community Answer
The mass of an oxygen molecule is about 16 times that of a hydrogen m...
Hence the correct choice is (3)
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