Rydberg Formula

If the state of an electron in a hydrogen atom is slightly perturbed, then the electron can make a transition to another stationary. The transition will emit a photon with a certain wavelength. If the electron state is characterized by the quantum number n the wavelength is given by the Rydberg formula.

(1/wavelength of the emitted photon) = (Rydberg constant)(1/(integer 1)² - 1/(integer 2)²)

The equation is:

1/λ = R(1/(n₁)² -1/(n₂)²)

with n₁ < n₂

Where:

R: Rydberg's constant (R=1.097 * 10⁷ m⁽⁻¹⁾)

λ: Wavelength of the emitted photon

n₁: integer 1

n₂: integer 2

Rydberg Formula Questions:

1) Assume an electron transition occurs from the n₁=2 to the n₂=3, what is the wavelength of the emitted photon?

Answer:

Substituting the data in the Rydberg formula

1/λ = (1.097 * 10⁷ m⁽⁻¹⁾)*(1/2 - 1/3)

1/λ = (1.097 * 10⁷ m⁽⁻¹⁾)*0.1666 = 0.182 *10⁷ (1/m)

λ = 5.47 * 10^(-7) m

2) Assume an electron transition occurs from the n₁=1and the wavelength of the emitted photon is 1.7 * 10^(-7) m, what is the integer number associated with the transition?

Answer:

Substituting the data in the Rydberg formula

1/1.7 * 10^(-7) m = (1.097 * 10⁷ m⁽⁻¹⁾)*(1- 1/n)

From this formula we find n

0.64 = 1 - 1/n

=1 - 0.64

=0.46

=1/0.46

=2.15

n ≈ 2