Question

Wavelength of light required to excite an electron in an hydrogen atom from level $n=1$ to $n=2$ will be:
(Given: Planck's constant $\left(h\right)=6.62\times {10}^{-34}\text{Js}$, speed of light $\left(c\right)=3\times {10}^8{\text{ms}}^{-1}$)

• A. $1.216\times {10}^{-7}\text{m}$
• B. $2.816\times {10}^{-7}\text{m}$
• C. $6.500\times {10}^{-7}\text{m}$
• D. $8.500\times {10}^{-7}\text{m}$

Answer 1

The correct option is A $1.216\times {10}^{-7}\text{m}$

$E=-2.178\times {10}^{-18}\left(\frac{Z^2}{n^2}\right)\text{J}$
For hydrogen, $Z=1$
So, $E_1=-2.178\times {10}^{-18}\left(\frac{1}{1^2}\right)\text{J}$
$E_2=-2.178\times {10}^{-18}\left(\frac{1}{2^2}\right)\text{J}$
Now, $E_2-E_1=\Delta E=2.178\times {10}^{-18}(\frac{1}{1^2}-\frac{1}{2^2})=\frac{hc}{\lambda }$
$\Rightarrow \lambda =1.216\times {10}^{-7}\text{m}$