Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm).

Engineering

Physics

Bohrs Model of Atom

Question

Consider a hydrogen atom with its electron in the n^th orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm).

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$KE = (\frac{1242}{90} - \frac{13 .6}{n^{2}})$ eV = 10.4 eV

$= 13 . 8 eV - \frac{13 .6}{n^{2}} eV$ = 10.4 eV

$(\frac{13 .6}{n^{2}}) eV = (13.8 - 10.4) eV = 3 . 4 eV$

So, n = 2