Question

When the electron in a hydrogen atom moves from n = 6 to n = 1, light with a wavelength of ________ nm is emitted?

Answer 1

First we find the energy level with the following formula, where a is the energy level, n1 is the final energy level, n2 is the starting energy level and r is Rydberg's constant in Joules
$a = r \times ( \frac{1}{n1} - \frac{1}{n2} )$
We insert the values

$a = 2.18 \times {10}^{ - 18} \times ( \frac{1}{ {1}^{2} } - \frac{1}{ {6}^{2} } )$
$= 2.12 \times {10}^{ - 18}$
The wavelength is found with this formula, where h is Planck's constant and c is the speed of light
$wavelength = \frac{h \times c}{a}$
Finally we insert the values
$\frac{6.626 \times {10}^{ - 34} \times 3 \times {10}^{8} }{2.12 \times {10}^{ - 18} } = 9.376 \times {10}^{ - 8}$
Which is the same as 93.8 nm