Question

Calculate the wavelength of radiation emitted when an electron falls from the n = 5 to n = 2 state in hydrogen. Is this light in the visible region of the electromagnetic spectrum? If it is, estimate its color. If it is not, what portion of the electromagnetic spectrum does it fall in?

Answer 1

Given:

initial orbit of electron=
`n_(i)=5`

final orbit of electron=
`n_(f) =2`

to find wavelength we use Rydberg equation:

1/λ
`=R(1/n_(f) ^2-1/n_(i) ^2)`

where R is Rydberg constant and it's value is
`R= 1.0973*10^7/m`

inserting all the values in formula

1/λ
`=(1.0973*10^7)(1/2^2-1/5^2)`

λ
`=3.14*10^-^7m= 3.14*10^-^5 cm`

for it's region and color look at given attached pictures