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
$(h=6.62\times {10}^{-34}Jsandc=3.0\times {10}^{8}m{s}^{-1})$

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