Asked for the radius of the Bohr orbit of hydrogen
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Line spectra, the Bohr atom and the old quantum theory
Problem
Asked for the radius of the n=3 Bohr orbit of hydrogen, a classmate writes:"Bohr's rule is mevr=nℏ, so the angular momentum is 3ℏ, three times the ground-state value. The radius is therefore three times the Bohr radius: r3=3a0=3×0.0529nm=0.159 nm."Take a fixed point nucleus, a circular orbit and the Coulomb force as the only force, with a0=0.0529 nm.
((a)) Identify the step that is wrong and say, by redoing the algebra, what the radius should be.
((b)) By what factor is that radius too small?