Question

Which of the following transitions would emit the shortest wavelength? select one; (a) n=2 to 1 (b) n=1 to 3 (c) n=1 to 2 (d) n=3 to 1

Answer 1

D.

Explanation:

To see a wavelength emitted, the electrons would have to move down energy levels in order to see an emission spectra, which limits our answer choices to A and D:

And since n=3 to n=1 has a higher energy emitted than from n=2 to n=1, the one with the higher energy emitted would have the shorter wavelength as Wavlength and Energy are inversely related.

Answer 2

`"(d) n = 3 to 1"`

Explanation:

Light is emitted when an electron jumps from higher orbit to lower orbit. So, `"(b)"` and `"(c)"` are not possible.

Wavelength emitted for transition `"n = 2"` to `"n = 1"` is

`1/λ_"a" = "R"[1/1^2 - 1/2^2] = "3R"/4`

`λ_"a" = 4/"3R" = 1.333/"R"`

Wavelength emitted for transition `"n = 3"` to `"n = 1"`

`1/"λ"_d = "R"[1/1^2 - 1/3^2] = "8R"/9`

`λ_"d" = 9/"8R" = 1.125/"R"`

`λ_"d" < λ_"a"`

∴ `"(d)"` is the correct option.