Question

Determine the wavelength associated with an electron having kinetic energy equal to 0.988 MeV. Electron mass is m_e=9x10^-31 kg, speed of light is 3x10⁸ m/s, 1 eV= 1.6x10^-19 J, h=6.6x10^-34 J.s, you must apply relativistic correction for mass.

Answer 1

We know that Kinetic Energy(K.E) of the electron relativistically as

.............................(1)

where m_o= rest mass of particle( here particle is electron)

thus m_o= m_e= 9 * 10^-31 kg

Also we know that in relativsitic correction,

  

where c= speed of light

and p= momentum of electron here

Using equation 1 in above,

  

  

  

  

then using all the values given in SI units, we get momentum as

  

Then using deBroglie equation,

Wavelenght associated with electron will be

(ANS)