Question

Question #aacb3

Answer 1

The energy of the photon is `1.549 × 10^"-19"color(white)(l) "J"`.

Explanation:

You use the Rydberg formula to calculate the energy.

Rydberg's original formula did not look directly at energies, but we can rewrite the formula to have these units.

The Rydberg formula in terms of energy is

`color(blue)(bar(ul(|color(white)(a/a) E = R(1/n_text(f)^2 - 1/n_text(i)^2)color(white)(a/a)|)))" "`

where

`R = "the Rydberg constant", 2.178 × 10^"-18"color(white)(l) "J"`, and
`n_text(i)` and `n_text(f)` are the initial and final energy levels.

In this problem,

`n_text(i) = 3`
`n_text(f) = 5`

∴ `E = 2.178 × 10^"-18"color(white)(l) "J" × (1/9 -1/25) = 2.178 × 10^"-18" color(white)(l)"J" × (25-9)/(25×9)`

`= 1.549 × 10^"-19"color(white)(l) "J"`