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?

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?

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

Question:  n ≈ ?

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