Question

Energy of an electron is given by $E=-2.178\times {10}^{-18}J\frac{Z^2}{n^2}$. 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. $2.816\times {10}^{-7}m$
• B. $6.500\times {10}^{-7}m$
• C. $8.500\times {10}^{-7}m$
• D. $1.214\times {10}^{-7}m$

Answer 1

Answer: (D)

$1.214\times {10}^{-7}m$

$E_1=\frac{hc}{\lambda }=2.178\times {10}^{-18}\times z^2\left[\frac{1}{1^2}\right]$
$E_2=\frac{hc}{\lambda }=2.178\times {10}^{-18}\times z^2\left[\frac{1}{2^2}\right]$
So, $E=E_2-E_1$
$E=\frac{hc}{\lambda }=2.178\times {10}^{-18}\times z^2[\frac{1}{1^2}-\frac{1}{2^2}]$
$\Rightarrow \lambda =1.214\times {10}^{-7}m$