### Q.9:- 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? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

**Answer:-**

Temperature of the helium atom, *T*_{He} = –20°C= 253 K

Atomic mass of argon, *M*_{Ar }= 39.9 u

Atomic mass of helium, *M*_{He} = 4.0 u

Let, (*v*_{rms})_{Ar} be the rms speed of argon.

Let (*v*_{rms})_{He} be the rms speed of helium.

The rms speed of argon is given by:

= 2523.675 = 2.52 × 10^{3} K

Therefore, the temperature of the argon atom is 2.52 × 10^{3} K.