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Unformatted text preview: Reading : Modern Physics 1, 2 Key concepts: Bohr model of hydrogen; photoelectric effect; deBroglie wavelength; uncertainty principle; nuclear decays; nuclear binding energy. 1. Comment on these early assumptions about atomic structure, indicating which one(s) survived when quantum mechanics was discovered in the 1920’s. a. Electrons circulate about the nucleus in defnite orbits. b. Radiation by an atom results From acceleration oF the electrons. c. The Frequency oF radiation is the same as the Frequency oF revolution oF an electron in its orbital motion. d. The energy carried oFF by radiation is equal to the loss oF energy by the radiating atom. 2. Comment on the Following statements about the restrictions imposed by the uncertainty principle. a. In principle, it renders the program oF Newtonian mechanics hopeless. b. It Forbids a system to have a precise value oF the angular momentum. c. It poses no problem to the practical use oF classical physics For systems oF macroscopic size. d. It means that the Bohr model’s use oF precise orbits For electrons in atoms cannot be valid. 3. There is another “uncertainty” rule, relating energy and time, usually written as Δ E ⋅ Δ t . It says the uncertainty in energy oF a state varies inversely with the average time For an appreciable change in that state. “Appreciable change” usually means change to a diFFerent state, e.g., a quantum jump in an atom, decay oF a radioactive nucleus, or decay oF an unstable particle into other particles. a. Since the ground state oF an atom is stable, its energy has no uncertainty, but an atom in an excited state will “decay” to the ground state, emitting a photon. ¡or a typical case the liFetime oF the excited state is about 10 − 8 s and the photon’s energy is about 1 eV. Estimate the Fractional uncertainty Δ E / E in the photon’s energy. b. Measurements oF the mass oF the ρ particle, For which mc 2 ≈ 750 MeV, show an uncertainty oF about 150 MeV. Assuming this is not just experimental uncertainties, estimate the liFetime oF this particle....
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