(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive an equation to show that there is a unique wavelength at which X-ray photons and electrons have the same energy. Calculate this wavelength and energy.

2. Relevant equations

Here's what I thought was relevant. There may be others!

For photons: E = hf = h c / λ

For electrons:

λ = h / p (de Broglie)

K.E. = ½ mv^2

p = mv

3. The attempt at a solution

p = √(2mE)

Substituting in de Broglie

λ = h / √(2mE)

E = h^2 / 2mλ^2

Equating energies

(h c / λ)X-ray = (h^2 / 2mλ^2)electron

Gathering the constants (c, h, 2 and m -- the rest mass of an electron)

(λ)X-ray = (h / 2cm) * (λ^2)electron

... which does not have a unique solution :-(

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Unique λ at which X-ray and electron have same energy

**Physics Forums | Science Articles, Homework Help, Discussion**