A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state.Find the wavelength of the emitted photon.
A)2.43 μm
B)1.46 μm
C)1.94 μm
D)2.92 μm

Question

Quizplus · Accepted Answer

The energy difference between the final and initial states can be calculated using the Rydberg formula:
1/λ = R(1/n1^2 - 1/n2^2)
where λ is the wavelength of the emitted photon, R is the Rydberg constant (1.097 × 10^7 m^-1), n1 is the initial state (n=20), and n2 is the final state (n=5).

1/λ = 1.097 × 10^7 m^-1 (1/20^2 - 1/5^2)
1/λ = 1.097 × 10^7 m^-1 (0.00225)
1/λ = 24,682.5 m^-1
λ = 4.05 × 10^-5 m
Convert to micrometers:
λ = 2.43 μm

Therefore, the correct answer is A) 2.43 μm.

A Hydrogen Atom Makes a Downward Transition from the N