Question

What is the wavelength (in nm) of the line in the spectrum of the hydrogen atom that arises from the transition of the electron from the orbital with n =5 to the orbital with n = 2?

Answer 1

433 nm

Step-by-step explanation:

To solve this problem we can use Rydberg's equation:

1 / λ = R *
`((1)/(n^(2)_(final))-(1)/(n^(2)_(initial))  )`

Where λ is the wavelength (in m), R is a constant (1.0974x10⁷ m⁻¹) and n are the initial and final states.

We put the data given by the problem and solve for λ:

1 / λ = 1.0974x10⁷ m⁻¹ *
`((1)/(2^2) -(1)/(5^2) )`

1 / λ = 2304540 m⁻¹

λ = 4.34x10⁻⁷ m

Converting m to nm:

4.34x10⁻⁷m * 10⁹nm / 1m = 433 nm