Question

Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be:

• A. $1.214\times {10}^{-7}\text{m}$
• 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 $1.214\times {10}^{-7}\text{m}$

$E=-2.178\times {10}^{-18}\left(\frac{Z^2}{n^2}\right)\text{J}$
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, $E_1-E_2$
i.e., $\Delta E=2.178\times {10}^{-18}(\frac{1}{1^2}-\frac{1}{2^2})=\frac{hc}{\lambda }$
Or, $\lambda =1.21\times {10}^{-7}\text{m}$

Where, 'h' is Planck's constant $(6.62\times {10}^{-34}\text{J s})$, 'c' is velocity of light $(3\times {10}^8\text{m/s})$.