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# 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).

Learn Exercise 13

Temperature of the helium atom, THe = –20°C= 253 K Atomic mass of argon, MAr = 39.9 u Atomic mass of helium, MHe = 4.0 u Let, (vrms)Arbe the rms speed of argon. Let (vrms)Hebe the rms speed of helium. The rms speed of argon is given by: … (i) Where, R is the universal gas constant TAr...

Temperature of the helium atom, THe = –20°C= 253 K

Atomic mass of argon, MAr = 39.9 u

Atomic mass of helium, MHe = 4.0 u

Let, (vrms)Arbe the rms speed of argon.

Let (vrms)Hebe the rms speed of helium.

The rms speed of argon is given by:

… (i)

Where,

R is the universal gas constant

TAr is temperature of argon gas

The rms speed of helium is given by:

… (ii)

It is given that:

(vrms)Ar = (vrms)He

= 2523.675 = 2.52 × 103 K

Therefore, the temperature of the argon atom is 2.52 × 103 K.

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