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catkin
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Homework Statement
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.
Homework Equations
For photons: E = hf = h c / λ
For electrons:
λ = h / p (de Broglie)
K.E. = ½ mv^2
p = mv
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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