130_notes.dvi

We can also compute the ground state radius of the Bohr orbit.

1

r

=

αmc^2

̄hc

r =

(137)(1973)

511000

= 0. 53 ̊A

This is also about the right radius. The name for this number, theBohr radius, persists to this
day despite the fact that Bohr’s assumption is wrong.

Although angular momentum is quantized in units of ̄h,the ground state of Hydrogen has zero
angular momentum. This would put Bohr’s electron in the nucleus.

Bohr fit the data, with some element of truth, but his model is WRONG.

2.5 Derivations and Computations

2.5.1 Black Body Radiation Formulas*

(Not yet available.)

2.5.2 The Fine Structure Constant and the Coulomb Potential

We will now grapple for the first time with the problem of which set of units to use. Advanced texts
typically useCGS unitsin which the potential energy is

V(r) =

−e^2

r

while theStandard International units

V(r) =

1

4 πǫ 0

−e^2

r

We can circumvent the problem by defining the dimensionlessfine structure constantα.

αSI =

1

4 πǫ 0

e^2

̄hc

≈

1

137

αCGS =

e^2

̄hc

≈

1

137

So in either set of units the Hydrogen potential is

V(r) =

−α ̄hc

r