An electron and a proton each have a thermal kinetic energy of 3kbt/2. calculate the de broglie wavelength of each particle at a temperature of 1800 k. (kb is boltzmann's constant, 1.38x10^-23 j/k). (1) wavelength of the electron = m (2) wavelength of the proton = m

Given:

Thermal Kinetic Energy of an electron,

= Boltzmann's constant

Temperature, T = 1800 K

Solution:

Now, to calculate the de-Broglie wavelength of the electron, :

             (1)

where

h = Planck's constant =

= momentum of an electron

= velocity of an electron

= mass of electon

Now,

Kinetic energy of an electron = thermal kinetic energy

                   (2)

Using eqn (2) in (1):

Now, to calculate the de-Broglie wavelength of proton, :

                            (3)

where

= mass of proton

= velocity of an proton

Now,

Kinetic energy of a proton = thermal kinetic energy

                              (4)                    

Using eqn (4) in (3):

thermal energy is the answer