A simplified model of a one-electron atom has the following allowed energy states…
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
A simplified model of a one-electron atom has the following allowed energy states (relative to the ionized state taken as 0 eV):
• n = 1: −10 eV (ground state)
• n = 2: −6 eV
• n = 3: −3 eV
An electron is initially in the n = 3 state and eventually returns to the ground state.
Assume that each radiative transition releases a photon whose energy equals the difference between the initial and final electronic energies. Ignore any non-radiative processes.
(a) Describe, in words, how the principle of energy conservation constrains the sum of photon energies in a two-step cascade transition from n = 3 to n = 1 through the intermediate n = 2 level.
(b) Explain why a single-step transition from n = 3 directly to n = 1 must produce a photon whose wavelength is shorter than the wavelength of either photon emitted in the two-step cascade.
(c) Suppose atoms in the ground state are irradiated with a continuous spectrum of white light. Identify which of the photon wavelengths from parts (a) and (b) would appear as absorption lines and explain your reasoning in terms of allowed electronic transitions.