Question

Question #29aac

Answer 1

`f = 3.085xx10^15Hz`

Explanation:

The energy from electrons rising and falling between shells in a hydrogen atom is given by the Rydberg formula.

`DeltaE = -E_0(1/n_f^2 - 1/n_i^2)`

where `DeltaE` is the change in energy, `E_0` is the Rydberg constant, `2.18xx10^-18"J"/"H atom"`, `n_f` is the final energy level and `n_i` is the initial energy level.

Plugging in the numbers, this gives us

`DeltaE = -2.18xx10^-18(1/1^2 - 1/4^2) =`
`-2.044xx10^-18"J"/"H atom"`

This energy is lost via photons emitted from the electrons. Energy of photons is given by

`E = hf = 6.626 xx 10^-34"Js" xx f`

so

`f = E/h = (DeltaE)/h = (2.044 xx 10^-18"J"/"H atom")/(6.626xx10^-34"Js")`
`= 3.085xx10^15"s"^-1`
`f=3.085xx10^15"Hz"`

This is the frequency of light given off by the hydrogen atom.