What is the wavelength of an electron travelling at 5x10^5 m/s?

1 Answer
Truong-Son N.
Jun 2, 2017

#lambda = "1.455 nm"#

You can use the de Broglie relation, since an electron has mass. What is the speed of a photon in vacuum with a wavelength of #"0.1 nm"#?

The relation is:

#lambda = h/p = h/(mv)#

where:

  • #lambda# is the wavelength in #"m"#.
  • #h = 6.626 xx 10^(-34) "J"cdot"s"# is Planck's constant.
  • #m# is the mass of the particle, such as the electron, in #"kg"#. The particle must have a mass for this relation to work.
  • #v# is the forward velocity of the particle, in #"m/s"#.

Hence, the wavelength is:

#lambda = (6.626 xx 10^(-34) "J"cdot"s")/((9.1094 xx 10^(-31) "kg")(5 xx 10^(5) "m/s"))#

We know that #"1 J" = "1 kg" cdot "m"^2"/s"^2#. So:

#color(blue)(lambda) = (6.626 xx 10^(-34) cancel"kg" cdot "m"^(cancel(2))"/"cancel"s")/((9.1094 xx 10^(-31) cancel"kg")(5 xx 10^(5) cancel"m""/"cancel"s"))#

#= 1.455 xx 10^(-9)# #"m"#

#=# #color(blue)("1.455 nm")#

Why does this not work on a photon?

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