Hydrogen Atom Energy Levels

"Someone told me that each equation I included in the book would halve the sales"
Stephen Hawking
(speaking about his book - A Brief History of Time)

The Bohr model leads to the prediction that the energy of the electron orbitting the proton is also only allowed to have certain specific values, E_n where,

n is an integer (the principal quantum number) and E₁ is the energy of the H atom in its ground state - when the electron orbits at the smallest radius (r).

E_n is the energy of the Hydrogen atom and the allowed energies are called energy levels. The first three energy levels are given in the table below.

n = 1	E₁ = 13.6 eV = 2.18 x 10^-18 J	r₁ = 5.3 x 10^-11 m
n = 2	E₂ = 3.4 eV = 0.54 x 10^-18 J	r₂ = 21.2 x 10^-11 m
n = 3	E₃ = 1.5 eV = 0.24 x 10^-18 J	r₃ = 47.6 x 10^-11 m

Note that energy level diagrams are usually plotted with negative values of energy. Negative energies mean that the system (electron and proton for Hydrogen) is "bound" . The larger the magnitude of the energy (the smaller the value of the energy) the more tightly the system is bound. Thus, the ground state (n = 1) of the Hydrogen atom is the most tightly bound configuration.

When n is very large the radius of the orbit tends to infinity and the energy of the atom tends towards zero. Under such circumstances the electron is "free" (not bound to the proton) and the atom is said to be ionised.

Why did the chicken cross the road ?
Werner Heisenberg: "We are not sure which side of the road the chicken was on, but it was moving very fast."

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu