Question

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

Answer 1

`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"`?

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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?