Determine the values of n

Question

A violet line is observed at  in the spectrum of atomic hydrogen. Determine the values of  n for the beginning and ending energy levels of the electron during the emission of energy that leads to this spectral line. n2= ? n1=?

Answer 1

1/λ = R_{H (}1/n₁² - 1/n₂²)

For the violet line in the hydrogen emission spectrum, λ = 410 nm

R_H = 1.09678x10^-2 nm^-1

1/410 = 1.09678x10^-2 (1/n₁² - 1/n₂²)

0.002439/1.09678x10^-2 = (1/n₁² - 1/n₂²)

0.22238 = (1/n₁² - 1/n₂²)

This is equivalent to

n₂² - n₁² / (n₁*n₂)² = 0.222/100

Two equations with 2 unknowns and solve for one of the unknowns:

n₂² - n₁² = 22.2

n₁*n₂ = sqrt 100