Question

Determine the wavelength of the light absorbed when an electron in a hydrogen atom makes a transition from an orbital in which n = 2 to an orbital in which n = 7.
Express the wavelength in nanometers to three significant figures.

Answer 1

Answer: The wavelength of light is $3.97\times 10^2nm$

Explanation:

To calculate the wavelength of light, we use Rydberg's Equation:

$\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )$

Where,

$\lambda$ = Wavelength of radiation

$R_H$ = Rydberg's Constant  = $1.097\times 10^7m^{-1}$

$n_f$ = Higher energy level = 7

$n_i$= Lower energy level = 2

Putting the values in above equation, we get:

$\frac{1}{\lambda }=1.097\times 10^7m^{-1}\left(\frac{1}{2^2}-\frac{1}{7^2} \right )\\\\\lambda =\frac{1}{0.2518\times 10^7m^{-1}}=3.97\times 10^{-7}m$

Converting this into nanometers, we use the conversion factor:

$1m=10^9nm$

So, $3.97\times 10^{-7}m\times (\frac{10^9nm}{1m})=3.97\times 10^2nm$

Hence, the wavelength of light is $3.97\times 10^2nm$