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