http://www.ck12.org Chapter 24. Atomic Physics
Asnincreases,n^12 →smaller, so the lines must fall closer together. Asnbecomes increasingly larger, the separation
between lines becomes so small that the spectrum begins to look continuous.
It was later found that Balmer’s formula could be extended to include electromagnetic radiation of smaller and larger
wavelengths (as anticipated by Rydberg) than those of visible light.
The Lyman Series, for example, describes the ultraviolet region of the electromagnetic spectrum for the hydrogen
atom, and has the same form as the Balmer series, as shown below.
1
λ=R
( 1
12 −
1
n^2)
,n= 2 , 3 ,...The Paschen series, as well, describes the infrared region of the electromagnetic spectrum for the hydrogen atom,
and also has the same form as the Balmer series, as shown below.
1
λ=R
( 1
32 −
1
n^2)
,n= 4 , 5 ,...Illustrative Example 25.2.1
What line spectrum frequency of light does the Lyman series predict forn=4?
Solution:
The formula for the Lyman series is:
1
λ=R
(
1
12
−
1
n^2)
,n= 2 , 3 ,.. .→1
λ=R
(
1
12
−
1
42
)
=
15
16
R→λ=16
15
1
R
λ= 9. 723 × 10 −^8 m( 97. 2 nm)But,c=fλ→f=λc=^3.^00 ×^10
8 ms
9. 723 × 10 −^8 m=^3.^085 ×^10(^14) Hz→ 3. 09 × 1014 Hz
Bohr’s Model
A 27-year-old Danish physicist Niels Bohr (1885-1962) was working in Rutherford’s laboratory, and attempted to
explain inconsistencies in the model where electrons were in orbit around a tiny, dense, positive nucleus.
According to classical electromagnetic theory, a charge spinning in a circle –like an orbiting electron –is being
accelerated back and forth, and it should radiate out electromagnetic waves just by orbiting. This did not hap-
pen. Hydrogen by itself radiated no light. Instead, it gave off light when energized, but only in specific lines
as described by Balmer. Bohr suspected that Rutherford’s atomic model would require some form of quantization
similar to the one described in the works of Planck and Einstein.
He postulated (that is, stated without proof) that electrons could not lose energy in a continuous fashion but rather
only when going from one energy state to another, as described by the Planck equation:
E=nh f
The energy of the atom must, therefore, be quantized.
Bohr also assumed that electrons could only take on specific (allowed) orbits about the nucleus, so the orbit radii
must be quantized as well.
Electrons radiate or absorb energy only when changing from one “allowed orbit” to another. He called the allowed
orbitsstationary states. An electron in each stationary state possesses a definite energy. Electrons, Bohr hypothe-
sized, could “jump” from one stationary state to another when absorbing or emitting a single photon. Not just any