At what temperature is the root-mean-square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at `-20^(@)C` ? The atomic masses of argon and helium are 39.9 a.m.u. and 4.0 a.m.u, respectively.

Explanation

To find the temperature at which the root-mean-square (rms) speed of an argon atom is equal to the rms speed of a helium atom at -20°C, we will follow these steps:

### Step 1: Write the formula for rms speed
The root-mean-square speed \( V_{rms} \) of a gas is given by the formula:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
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