Question

Assertion: The molecules of a monoatomic gas has three degrees of freedom.
Reason: The molecules of a diatomic gas has five degrees of freedom.
A. Both Assertion and Reason are true and Reason is the correct explanation of the Assertion.
B. Both Assertion and Reason are true but Reason is not the correction explanation of the Assertion.
C. Assertion is true but the Reason is false.
D. Assertion is false but the Reason is true.

Answer 1

Hint:Molecules of a monoatomic gas can move in any direction in space, but molecules of a diatomic gas can move in any direction in space and they can rotate about the coordinate axes as well. Use this concept to solve the given Assertion-Reason question.



Complete answer:
Consider a monoatomic molecule like Helium $\left( {He} \right)$ .
It can move in all three directions in a space. This means that it has translational motion in every direction in space.
However, it cannot rotate about any axis as it consists of only one atom.
Thus, the degree of freedom for molecules of monoatomic gas is 3.
Hence, the Assertion is true.
Now, consider a diatomic molecule like oxygen $\left( {{O_2}} \right)$ .
Like any monoatomic molecule, it can also move in all three directions in space, thus, having translational motion in every direction in space.
It can also rotate about the coordinate axis, existing in space. The axis should be perpendicular to its own axis though.
This makes a diatomic molecule to have two additional degrees of freedom.
Thus, the degree of freedom for molecules of a diatomic gas is 5.
Hence, the Reason is true as well.
We can clearly see that both the assertion and reason are true but the reason is not the correct explanation for the assertion.
Thus, the correct option is B.



Note: Degree of freedom of a gas molecule is the total number of possible ways a gas molecule moves, rotates, or vibrates in space. At high temperatures, the molecules of a diatomic gas start to vibrate, making its degree of freedom 6.