We have a relation to find kinetic energy of a gas molecule at any Temperature which is

Where E_K is the kinetic energy of a particle at temperature T and K is boltzmann constant

K = 1.38 × 10^-23 JK^-1

And we know Kinetic energy of a particle is given by the relation

Where v_rms is the root meansquare speed of the particle and m is the mass of the particle

So equating both equations we have

On solving we get the root meansquare speed of the particle as

Where V_rms is the root mean square speed of the particle of mass m at temperature T and K is boltzmann constant

K = 1.38 × 10^-23 JK^-1

Here the temperature is

T = 300K

We are given the particle is a nitrogen molecule (N₂) mass of the Nitrogen atom is

m_N = 14.0076 u

so mass of N₂ molecule is

m = 2 × 14.0076 u = 28.0152 u

converting it to Kg

we know 1 u = 1.66 × 10^-27 Kg

so mass of Nitrogen molecule is

m = 28.0152 × 1.66 × 10^-27Kg = 46.50 × 10^-27Kg

= 4.650 × 10^-26Kg

We know de-Broglie wavelength of a particle is given by relation

where