Question #140790
Calculate the de broglie wavelength associated with an electron moving with velocity of 1/10 th the velocity of the light
1
Expert's answer
2020-10-28T08:41:49-0400

Velocity of the electron v=110×cv = \frac{1}{10} \times c

v=110×3×108=3×107  m/sv = \frac{1}{10} \times 3 \times 10^8 = 3 \times 10^7 \; m/s

Mass of electron m=9.1×1031  kgm = 9.1 \times 10^{-31} \;kg

De Broglie equation:

λ=hp=hmvλ = \frac{h}{p} = \frac{h}{mv}

h – Plank’s constant

h=6.62×1034  Jsh = 6.62 \times 10^{-34} \;Js

p – momentum

v – velocity of electron

λ=6.62×10349.1×1031×3×107λ = \frac{6.62 \times 10^{-34}}{9.1 \times 10^{-31} \times 3 \times 10^{7}}

λ=2.24×109λ = 2.24 \times 10^{-9}

109  m=nm10^{-9} \;m = nm

λ=2.24  nmλ = 2.24 \;nm


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