Calculate the de Broglie wavelength of an electron moving at 40 m·s −1.
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Step 1 : Determine what is required and how to approach the problem
We are required to calculate the de Broglie wavelength of an
electron given its speed. We can do this by using:
λ = h/mv
Step 2 : Determine what is given
We are given:
• The velocity of the electron v = 40 m · s−1
and we know:
• The mass of the electron me = 9,11 × 10−31 kg
• Planck’s constant h = 6,63 × 10−34 J · s
Step 3 : Calculate the de Broglie wavelength
λ = h/mv
=( 6,63 × 10−34 J · s)/(9,11 × 10−31 kg)(40 m · s−1)
= 1,82 × 10−5 m
= 0,0182 mm
Although the electron and cricket ball in the two previous examples are travelling at the same velocity the de Broglie wavelength of the electron is much larger than that of the cricket ball. This is because the wavelength is inversely proportional to the mass of the particle.