# Classical atomic models

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# On absorbing a photon by $\mathrm{H}-$atom, an electron got excited and reached fifth orbit. When the excited atom returned to its ground state, visible and other quanta were emitted. Radiation of what wavelength must have been emitted ? Explain it.

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Solution

## Visible region indicates the fall of electron to the second orbit. After this, the transition  must take place for the atom to return to its ground state  Hence:                                    $\begin{array}{l}\stackrel{-}{\mathrm{\nu }}=109678\left(\frac{1}{{1}^{2}}-\frac{1}{{2}^{2}}\right){\mathrm{cm}}^{-}\\ =82258{\mathrm{cm}}^{-}\end{array}$or                               $\frac{1}{\lambda }=\frac{1}{82258{\mathrm{cm}}^{-}}=1.22×{10}^{-5}\mathrm{cm}$                                      $\begin{array}{l}=1.22×{10}^{-5}\mathrm{cm}×\frac{{10}^{8}{\mathrm{A}}^{\mathrm{o}}}{1\mathrm{cm}}\\ =1220{\mathrm{A}}^{\mathrm{o}}\end{array}$

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The ground state energy of hydrogen atom is -13.6 eV. The Energy of second exited state of ${\mathrm{He}}^{+}$ ion in eV is