At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the r.m.s. speed of a helium gas atom at `-20^(@) C` ? (Atomic mass of Ar = 39.9 u, of He = 4.0 u).

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 can follow these steps:

### Step 1: Understand 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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