1. Use kinetic theory for total translational kinetic energy

For an ideal gas, the total kinetic energy of molecular translation depends only on the number of moles and temperature:

$K = \frac{3}{2}NRT$

This is true whether the gas is monoatomic or diatomic, because translational kinetic energy is always

$\frac{3}{2}RT \text{ per mole}.$

2. Initial state

Initially, there are $N$ moles of diatomic gas at temperature $T$.

So initial total kinetic energy is

$K_i = \frac{3}{2}NRT$

3. Final state

Temperature remains constant, and $n$ moles of diatomic gas are converted into monoatomic gas.

But the total number of moles remains $N$; only the nature of $n$ moles changes from diatomic to monoatomic.

Since translational kinetic energy depends only on total moles and temperature,

$K_f = \frac{3}{2}NRT$

4. Change in total kinetic energy

$\Delta K = K_f - K_i = \frac{3}{2}NRT - \frac{3}{2}NRT = 0$

5. Check options

• A: $\frac{1}{2}nRT$ ❌
• B: $0$ ✅
• C: $\frac{3}{2}nRT$ ❌
• D: $\frac{5}{2}nRT$ ❌

Therefore, the correct answer is:

$\boxed{0}$

So Option B is correct.

6. Comparison with stored answer

Stored correct answer: A

My derived answer: B

The stored answer likely confuses total internal energy with total kinetic (translational) energy. If the question asks specifically for total kinetic energy of the gas, then for an ideal gas at constant temperature it remains unchanged, regardless of whether molecules are monoatomic or diatomic.