Question

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

• 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

Answer: (A)

Given, in the question $E=-2.178\times 10^{-18}J\left[\frac{Z^2}{n^2}\right]$
For hydrogen $Z=1$,
So, $E_1=-2.178\times 10^{-18}J\left[\frac{1}{1^2}\right]$
$E_2=-2.178\times 10^{-18}J\left[\frac{1}{2^2}\right]$
Now, $E_1-E_2$
i.e. $\Delta E=2.178\times 10^{-18}\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{hc}{\lambda }$
$2.178\times 10^{-18}\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{6.62\times 10^{-34}\times 3.0\times 10^8}{\lambda }$
$\therefore \lambda \approx 1.21\times 10^{-7}m$