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 $E = \frac{h c}{\lambda}$ ?
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What is the lambda associated with an electron? – simon at rcl Apr 16 '22 at 13:57
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The electrons in a hydrogen atom do not have a wavelength as their wavefunction is not a plane wave. Presumably this is using the Bohr model and calculating the wavelength the electrons would have if the Bohr model were an accurate description. Anyhow, the relationship E = hc/λ only applies to massless particles, while the de Broglie equation λ = h/p applies to all particles massive or otherwise. – John Rennie Apr 16 '22 at 15:00
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Related : About de Broglie relations, what exactly is E? Its energy of what?. – Frobenius Apr 17 '22 at 11:35
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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.
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