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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?
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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.
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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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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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 bea)v0/16b)v0/4c)4v0d)16v0Correct answer is option 'C'. Can you explain this answer?
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