Question

Compare the wavelengths of an electron (mass=9.11x10^-31 kg) and a proton, (mass=1.67x10^-27 kg) each having (a) a speed of 8.38x10^6 m/s and (b) a kinetic energy of 1.39x 10^-15 J

Answer 1

To calculate the wavelengths, we use the de Broglie Equation. This equation elates kinetic energy, mass and wavelength. It is expressed as:

λ = h/√(2)KE(m)

For the electron,
λ = 6.626 x 10¯34 J s / √2(1.39x10^-15 J)(9.11x10^-31 kg) = 2.62 x 10^11 m 

For the proton,
λ = 6.626 x 10¯34 J s / √2(1.39x10^-15 J)(1.67x10^-27 kg) = 1.43 x 10^8 m

Electron has a higher wavelength than a proton.