What is the associated debroglie wavelength of a h2 molecule moving on one direction with kinetic energy of (3/2 kt) at 30 k

The de-Broglie's wavelength of a hydrogen molecule is

Explanation:

Kinetic energy is the measure of temperature of the system.

The equation used to calculate kinetic energy of a particle follows:

where,

E = kinetic energy of the particles  = ?

k = Boltzmann constant  =

T = temperature of the particle = 30 K

Putting values in above equation, we get:

Conversion factor used:  1 kg = 1000 g

1 mole of hydrogen gas has a mass of 2 grams or  

According to mole concept:

number of molecules occupy 1 mole of a gas.

As, number of hydrogen molecules has a mass of

So, 1 molecule of hydrogen will have a mass of =

where,

= De-Broglie's wavelength = ?

h = Planck's constant =

m = mass of 1 hydrogen molecule =

= kinetic energy of the particle =

Putting values in above equation, we get:

   (Conversion factor: )

Hence, the de-Broglie's wavelength of a hydrogen molecule is