The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.
Given:
Mass of an Electron = 9.1 × 10–31 kg
Kinetic Energy, K.E. = 3.0 × 10–25 J
1/2 mv2 = kinetic Energy
Where
m = mass of electron
v = velocity of electron
v2 = [2× 3.0 × 10–25] / [9.1× 10-31]
= [6.0 × 10–25] / [9.1× 10-31]
v2 = 659.3406 × 103
Therefore v = √ [659.3406 × 103]
v = 811.99 m/s
According to the de Broglie’s Equation:
λ = h/mv
Where,
λ = wavelength of moving particle
m = mass of electron
v= velocity of particle
h= Planck’s constant [6.62× 10-34]
λ = {[6.62× 10-34] / [9.1× 10-31] × [811.99]}
= {[6.62× 10-34] / [7.389 × 10-28]
= 8.959× 10-7 m
Therefore, the wavelength is 8.96× 10-7 m