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

This is from Advanced Physics by Adams and Allday. Spread 8.34, Q 4.

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

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

Separating out the constants c, h, 2 and m (where m is the rest mass of an electron)

(λ)X-ray = (h / 2cm) * (λ^2)electron

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

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

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