Question

What is the energy in joules required to shift the electron of the hydrogen atom from the first Bohr orbit tothe fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? the ground state electron energy is $\text{- 2}\text{.18}\times {\text{10}}^{\text{- 11}}\text{ergs}\text{.}$

Answer 1

Grand state, $n=1$, energy is given by,

$E_1=-2.18\times {10}^{-11}ergs$

Now, energy of the $n=S$ ($5^{th}$ orbit} is given by,

$E_s=\frac{E_1}{(S{)}^2}$

$=\frac{-2.18\times {10}^{-11}}{2S}ergs$

$=-0.0872\times {10}^{-11}ergs$

Energy required to go to the $5^{th}$ orbit

$=E_S-E_1$

$=-0.0872-(-2.18)\times {10}^{-11}ergs$

$=2.0928\times {10}^{-11}ergs$

Now, $1erg={10}^{-7}J$

$\Rightarrow 2.0928\times {10}^{-11}ergs=2.0928\times {10}^{-18}J$

For wavelength, $\frac{1}{\lambda }=R[\frac{1}{(1{)}^2}=\frac{1}{(S{)}^2}]$

where, $R=1.0973\times {10}^{5}c{m}^{-1}$
$\Rightarrow \frac{1}{\lambda }=1.0973\times {10}^5[1-\frac{1}{2S}]$

$\Rightarrow \lambda =9.49\times {10}^{-5}cm$

or, $\simeq 9.5\times {10}^{-7}m$