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So we have to find the ratio of wavelength of electrons in 1st and 4th orbit of an atom. Why do we have to use de Broglie wavelength and not $E = \frac{h c}{\lambda}$ ?

Qmechanic
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rrg_24
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1 Answers1

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The equation $$E = \frac{hc}{\lambda}$$ applies only to particles with no invariant mass (like photons), where $f = \frac{E}{h} =\frac{c}{\lambda}$.

For particles with a non-zero mass (like electrons), the following relations hold: $$\lambda = \frac{h}{p} = \frac{h}{\gamma mu}$$ $$f = \frac{E}{h} = \frac{\gamma mc^2}{h}$$ where $\gamma$ is the Lorentz factor.

Hope this helps.

Cross
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