Find the de Broglie wavelength (in nm) associated with an electron that is moving with a velocity of 5230 km/s. The electron rest mass is 9.11 x 10⁻³¹ kg. Note, electrons having this speed would need to be treated as waves in atoms because the wavelength is on the order of the size of atoms.

The de brogllie wavelength is given as

λ = h/mv

where

λ is the de broglie wavelenth

h is the plank constant given as 6.62 * 10-34 m² kg / s

m is the mass of the particle = 9.11 x 10⁻³¹ kg

v is the velocity with which the particle moves = 5230 km/s. which as to be converted to m/s by multiplying it by 1000 to give 5230000m/s

hence

λ = 6.62 * 10-34 / 5230000 * 9.11 x 10⁻³¹ =

1.39 * 10^{-10}m

but since the answer must be in nm, we multiply 1.39 * 10^{-10}m by 10^{9}

then we get 0.139nm