Question

Wavelength of one radiation is 6000$\stackrel{\text{o}}{\text{A}}$. what is the wavelength of the other radiation?

Answer 1

Ground state energy$=E_1=-2.18\times {10}^{-11}$

=$-2.18\times {10}^{-11}\times {10}^{-7}$

$=-2.18\times {10}^{-18}Joules$

Also, the energy required to shift the electron from n=1 to n=5 is given as $\Delta E=E_5-E_1$

The expression for the energy of hydrogen of electron is

$E_n$= $\frac{-{2n}^2{me}^4{z}^2}{n^2{n}^2}$

$\Delta E=E_5-E_1$

$=\frac{-2.18\times {10}^{-18}{\left(11\right)}^2}{{\left(5\right)}^2}-(-2.18\times {10}^{-18})$

$=2.18\times {10}^{-18}[1-\frac{1}{25}]$

$=2.18\times 10{}^{-}18\left[\frac{24}{25}\right]$

$=2.0928\times {10}^{-18}Joules$

wavelength of emitted light=$\frac{hc}{E}$

$=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{2.0928\times {10}^{-18}}$

$=9.498\times {10}^{-18}m$