Question

What is the energy absorbed when the electron in a hydrogen atom jumps from `n = 3` to `n=8`?

Answer 1

The energy is `2.080 × 10^"-19"color(white)(l) "J"`.

Explanation:

We use the Rydberg formula to calculate the transition energies of a hydrogen atom.

`color(blue)(bar(ul(|color(white)(a/a) ΔE = R_E(1/n_i^2 - 1/n_f^2)color(white)(a/a)|)))" "`

where

`ΔE` = energy absorbed or released
`R_E` = Rydberg constant in energy units
`n_i` = initial energy level
`n_f` = final energy level

In your problem,

`R_E = 2.178 × 10^"-18"color(white)(l) "J"`
`n_i = 3`
`n_f = 8`

∴ `ΔE = 2.178 × 10^"-18"color(white)(l) "J"(1/3^2 - 1/8^2) = 2.178 × 10^"-18"color(white)(l) "J"(1/9 - 1/64)`

`= 2.178 × 10^"-18" color(white)(l)"J"((64-9)/(64 × 9)) = 2.178 × 10^"-18"color(white)(l) "J" × 55/(64 × 9)`

`= +2.080 × 10^"-19"color(white)(l) "J"`

The positive sign tells you that the atom has absorbed energy.