Question

Energy of an electron is given by $E=-2.178\times {10}^{-18}J\times \frac{Z^2}{n^2}$:
Wavelength of light required to excite an electron in an hydrogen atom from level $n=1$ to $n=2$ will be ($h=6.62\times {10}^{-34}Js$ and $c=3.0\times {10}^{8}m{s}^{-1}$ )

• A. $1.214\times {10}^{-7}m$
• B. $2.816\times {10}^{-7}m$
• C. $6.500\times {10}^{-7}m$
• D. $8.500\times {10}^{-7}m$

Answer 1

The correct option is A $1.214\times {10}^{-7}m$

Given, in the question:
$E=-2.178\times {10}^{-18}J\times \frac{Z^2}{n^2}$
For hydrogen $Z=1$,
$E_1=-2.178\times {10}^{-18}J\times \frac{1^2}{1^2}=-2.178\times {10}^{-18}J\times \frac{1}{1}$
$E_2=-2.178\times {10}^{-18}J\times \frac{1^2}{2^2}=-2.178\times {10}^{-18}J\times \frac{1}{4}$
Now, $E_1-E_2$:
= $-2.178\times {10}^{-18}J\times [\frac{1}{1}-\frac{1}{4}]$ = $\frac{hc}{\lambda }$
⇒ $-2.178\times {10}^{-18}J\times [\frac{1}{1}-\frac{1}{4}]$
=$\frac{6.62\times {10}^{-34}\times 3.0\times {10}^8}{\lambda }$
⇒ $\lambda =1.21\times {10}^{-7}m$