Question

Determine the wavelength of incident electromagnetic radiation required to cause an electron transition from the n = 5 to the n = 7 level in a hydrogen atom.

Answer 1

The correct answer is: wavelength = 4562 nm

Explanation:

Rydberg's formula is given as:
$\frac{1}{\lambda} = R[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ]$ --- (1)

Where 
R = Rydberg's constant = 1.096 * 10^7 per meter
$n_1$ = 5
$n_2$ = 7

λ = Wavelength

Plug in the values in (1):

(1)=> $\frac{1}{\lambda} = (1.096 * 10^7)[ \frac{1}{5^2} - \frac{1}{7^2} ]$

$\frac{1}{\lambda} = (1.096 * 10^7)[ 0.04 - 0.020 ] \\ \lambda = \frac{1}{(1.096 * 10^7)[0.020 ]} \\ \lambda = 4562 nm$