MHT CET · Physics · Kinetic Theory of Gases

The speed of oxygen molecule in a gas is u,If the temperature is doubled and the molecule dissociates into two atoms, the speed will be

A 4u
B u
C 2u
D u $\sqrt{2}$

Verified Solution

Answer & Solution

Correct Answer

(C) 2u

Step-by-step Solution

Detailed explanation

rms speed of

O_{2}

molecule = u
i.e.,

u = \sqrt{\frac{3 R T}{M}}

where,

T

= temperature and

M

= molecular mass.
When temperature is doubled, then

O_{2}

dissociates into two atoms.
Hence, the atomic mass of oxygen atom,

(M^{'}) = \frac{M}{2}

∴

rms velocity of oxygen atom

u^{'} = \sqrt{\frac{3 R T^{'}}{M^{'}}} = \sqrt{\frac{3 R . 2 T}{\frac{M}{2}}} [\begin{matrix} T^{'} = & 2 T \\ M^{'} = & \frac{M}{2} \end{matrix}]

= 2 \sqrt{\frac{3 R T}{M}} = 2 u

[from Eq. (i)]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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