Given below are two statements. One is labelled as Assertion (A) and the other is labelled as reason (R).

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Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are true but (R) is not the correct explanation of (A)

(A) is true but (R) is false

Both (A) and (R) are false

answer is B.

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Detailed Solution

Argon exists as individual atoms, rather than as molecules composed of multiple atoms. This is because argon is an inert gas with a completely filled valence electron shell, making it very stable and unlikely to bond with other atoms to form molecules.

The ratio of molar heat capacities of argon is 1.67, which refers to the ratio of the heat capacities at constant pressure (C_p) and constant volume (C_v) for argon. This ratio is also known as the adiabatic index or the ratio of specific heats (γ).

For an ideal monoatomic gas such as argon, the value of γ is given by:

γ = C_p/C_v = (5/2) + 1 = 1.67

Here, the first term (5/2) represents the contribution of the translational motion of the atoms in three dimensions, and the second term (1) represents the contribution of the rotational motion of the atoms about their own axes. Since argon is a monoatomic gas, it has no vibrational degrees of freedom.

Therefore, the statement "Atomicity of argon is unity" and the given ratio of molar heat capacities for argon (γ = 1.67) are consistent with each other.

So, both (A) and (R) are true, but (R) is not the correct explanation of (A).

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