Physical Chemistry , 1st ed.

substitute for the radius in the expression for the total energy, equation 9.31,
to obtain

Etot

8 

m

2

0 n

ee

2

4

h^2

 (9.35)

or the total energy of the hydrogen atom. It is simple to demonstrate that this
expression has units of energy:



(C^2 /J

k

m

gC

)^2

4

(Js)^2

kg

C

C

4

4

J^2

J

s

2

2

m^2

kg

s



2

m^2 J

Again, note that the total energy, like the radius, is dependent on a collection
of constants and a number,n, that is restricted to integer values.The total en-
ergy of the hydrogen atom is quantized.
Finally, Bohr’s assumption 4 dealt with changes in energy levels. The differ-
ence between a final energy,Ef, and an initial energy,Ei, is defined as E:

EEfEi (9.36)

9.9 Bohr’s Theory of the Hydrogen Atom 265

4.7 6 Å

2.12Å

0. 529 Å

n

L=h/ 2 J•s

EE=– –^1

nn=2

/ 2  •s

E – –^1

n

L  Js

EE=– –^1

p+

Figure 9.19 The Bohr model of the hydrogen atom—shown here with its three lowest-energy
states—is not a correct description, but it was a crucial step in the development of modern quan-
tum mechanics.