The root mean squared velocity of a gas is given by
v=M3RT
⇒v∝T
Let
T1=300KT2=600K
Taking velocity ratios at the given temperatures,
v2v1=T2T1=600300=21
The de Broglie wavelength is given by λ=mvh. So,
λ∝v1
The ratio of the wavelengths is
λ2λ1=(v1v2)=12
⇒λ2=(21λ1)