a. Starting with the expression f t 1 for a wave packet, find an expression for the product E t for a photon. b.

a. Starting with the expression Δf Δt ≈ 1 for a wave packet, find an expression for the product ΔE Δt for a photon.
b. Interpret your expression. What does it tell you?
c. The Bohr model of atomic quantization says that an atom in an excited state can jump to a lower-energy state by emitting a photon. The Bohr model says nothing about how long this process takes. You’ll learn in Chapter 41 that the time any particular atom spends in the excited state before emitting a photon is unpredictable, but the average lifetime Δt of many atoms can be determined. You can think of Δt as being the uncertainty in your knowledge of how long the atom spends in the excited state. A typical value is Δt ≈ 10 ns. Consider an atom that emits a photon with a 500 nm wavelength as it jumps down from an excited state. What is the uncertainty in the energy of the photon? Give your answer in eV.
d. What is the fractional uncertainty ΔE/E in the photon’s energy?