The root mean square speed of the molecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociates into two atoms. The new root mean square speed of the atom is

Explanation

To solve the problem, we need to find the new root mean square (RMS) speed of the atoms after the diatomic gas dissociates when the temperature is doubled. Let's break this down step by step.

### Step 1: Understand the initial conditions
The root mean square speed of the molecules of the diatomic gas is given as \( v \). The formula for the root mean square speed \( v_{\text{rms}} \) of a gas is given by:

\[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
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