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.

Question

Chemistry

Dominick Pena

3 October, 17:29

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.

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Raelynn Bolton · Answer 1

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