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Assertion: Each vibrational mode gives t...

Assertion: Each vibrational mode gives two degrees of freedom.
Reason: By law of equipartition of energy, the energy for each degree of freedom in thermal equlibrium is `2k_(B)T.`

A

If both assertion and reason are true and reason is the correct explanation os assertion.

B

If both assertion and reason are true but reason is not be correct explanation of assertion.

C

If assertion is true but reason is false.

D

If both assertion and reason are false.

Text Solution

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The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that "each vibrational mode gives two degrees of freedom." - In kinetic theory, each vibrational mode of a molecule contributes two degrees of freedom: one for kinetic energy (due to the motion of the atoms in the mode) and one for potential energy (due to the displacement of the atoms from their equilibrium positions). - Therefore, the assertion is **true**. ### Step 2: Analyze the Reason The reason states that "by the law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is `2k_B T`." - The law of equipartition of energy actually states that each degree of freedom contributes an energy of `1/2 k_B T` for kinetic energy and `1/2 k_B T` for potential energy. Therefore, for each vibrational mode, which has two degrees of freedom (kinetic and potential), the total energy contribution is `1/2 k_B T + 1/2 k_B T = k_B T`. - The statement in the reason is incorrect because it states `2k_B T` instead of `k_B T`. Hence, the reason is **false**. ### Step 3: Conclusion - The assertion is true, and the reason is false. Therefore, the correct answer to the question is that the assertion is true, but the reason is false. ### Final Answer - Assertion: True - Reason: False - Correct Answer: Assertion is true, Reason is false. ---
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that "each vibrational mode gives two degrees of freedom." - In kinetic theory, each vibrational mode of a molecule contributes two degrees of freedom: one for kinetic energy (due to the motion of the atoms in the mode) and one for potential energy (due to the displacement of the atoms from their equilibrium positions). - Therefore, the assertion is **true**. ...
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