For hydrogen with the proton held fixed

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The hydrogen atom

Problem

For hydrogen with the proton held fixed, the levels derived in this chapter are

E_n = -13.6\ \mathrm{eV}/n^2

. Take

hc = 1240\ \mathrm{eV\,nm}

and

a_0 = 0.0529\ \mathrm{nm}

. The electron has spin one-half, with two values of

m_s

. Fine structure and the reduced-mass correction are ignored, and each transition emits one photon whose energy equals the difference of the two levels. ((a)) An atom falls from

n = 2

n = 1

. Find the wavelength of the emitted line, in nm. ((b)) The ground-state radial function is

R_{10}(r) \propto e^{-r/a_0}

. Using the radial probability density

P(r) = |R_{10}(r)|^2r^2

, find the most probable radius, in nm. ((c)) How many states does the

n = 1

level contain, first without counting spin and then counting spin?

Related theory

Quantum Mechanics

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