The degree of freedom for tri atomic gas is:a)6b)4c)5d)3Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Degrees of freedom are the ways in which a molecule of the gas can execute motion.
So in case of triatomic gas molecule:
1. It can translate (move) in all 3 dimensions, which accounts for 3 degrees of freedom (since there are 3 dimensions in which it could translate (move)).
2. This molecule can also revolve with Moment of Inertia ≠ 0 around all three axes, x, y, and z, which accounts for another 3 degrees of freedom (since there are 3 axes of rotation).

Answer

Degrees of freedom are the ways in which a molecule of the gas can execute motion.
So in case of triatomic gas molecule:
1. It can translate (move) in all 3 dimensions, which accounts for 3 degrees of freedom (since there are 3 dimensions in which it could translate (move)).
2. This molecule can also revolve with Moment of Inertia≠0around all three axes, x, y, and z, which accounts for another 3 degrees of freedom (since there are 3 axes of rotation).

Answer

The degree of freedom for a molecule refers to the number of independent ways in which it can move or store energy. In the case of a triatomic gas, which consists of three atoms, each atom can move independently in three dimensions (x, y, and z). However, there are certain constraints on the motion of the atoms due to the molecular structure, such as bond lengths and bond angles.

In a triatomic gas, there are three atoms connected by two bonds, forming a linear or bent structure. Let's consider the linear case first.

Linear Triatomic Gas:
In a linear triatomic gas, the atoms are arranged in a straight line. The central atom is bonded to the two terminal atoms. In this case, the central atom can move freely in three dimensions (x, y, and z), contributing 3 degrees of freedom. The terminal atoms, on the other hand, can only move in two dimensions (x and y) because their motion is restricted along the bond axis. Each terminal atom contributes 2 degrees of freedom. Therefore, the total degrees of freedom for a linear triatomic gas is 3 + 2 + 2 = 7.

Bent Triatomic Gas:
In a bent triatomic gas, the atoms are arranged in a non-linear fashion. The central atom is bonded to the two terminal atoms, forming a bond angle. One degree of freedom is lost due to the constraint of the bond angle. The central atom can still move freely in three dimensions (x, y, and z), contributing 3 degrees of freedom. The terminal atoms, however, can only move in two dimensions (x and y) due to the restriction along the bond axis. Each terminal atom contributes 2 degrees of freedom. Therefore, the total degrees of freedom for a bent triatomic gas is 3 + 2 + 2 - 1 = 6.

Conclusion:
In conclusion, the degree of freedom for a triatomic gas depends on its molecular structure. For a linear triatomic gas, the degree of freedom is 7, while for a bent triatomic gas, the degree of freedom is 6. Therefore, the correct answer to the question is option 'A', which states that the degree of freedom for a triatomic gas is 6.

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