What is the energy in joules,required to shift the electron of the hydrogen atom from the first Bohr orbit to the 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 $-2.18 \times 10^{-11} \ erg$.

The energy $(E)$ of the $n^{\text{th}}$ Bohr orbit of an atom is given by:
$E_{n} = \frac{-(2.18 \times 10^{-18} \ J) Z^{2}}{n^{2}}$
Given,ground state energy $= -2.18 \times 10^{-11} \ erg = -2.18 \times 10^{-18} \ J$.
Energy required to shift the electron from $n=1$ to $n=5$ is:
$\Delta E = E_{5} - E_{1} = -2.18 \times 10^{-18} [\frac{1}{5^{2}} - \frac{1}{1^{2}}]$
$\Delta E = -2.18 \times 10^{-18} [\frac{1}{25} - 1] = -2.18 \times 10^{-18} [-\frac{24}{25}]$
$\Delta E = 2.0928 \times 10^{-18} \ J$.
When the electron returns to the ground state,the energy emitted is equal to the energy absorbed,$\Delta E = 2.0928 \times 10^{-18} \ J$.
The wavelength $(\lambda)$ of the emitted light is given by:
$\lambda = \frac{hc}{\Delta E} = \frac{(6.626 \times 10^{-34} \ J \cdot s) (3 \times 10^{8} \ m/s)}{2.0928 \times 10^{-18} \ J}$
$\lambda = 9.498 \times 10^{-8} \ m$.