BioPHYSICAL chemistry

it was realized in 1885 that the frequencies associated with the lines of

the spectrum of hydrogen could be mathematically related to each other

by the relationship:

(9.15)

where the frequencies are written as wavenumbers (see Chapter 11). These

lines are now known as the Balmer lines. After the lines in the ultraviolet

region were discovered, yielding the Lyman and Paschen series, Johannes

Rydberg noted in 1890 that all of the lines could be described using:

(9.16)

where n 1 =1 for the Lyman series and n 1 =2 for the Balmer series. The

constant RHis now known as the Rydberg constant and has a value of

109,677 cm−^1.

Despite knowing that the frequencies were related to each other, an

understanding of the physical principle did not follow from the simple

pictures of the atomic structure as groupings of particles. Neils Bohr

proposed that discrete emission naturally follows from the concept of elec-

trons revolving around the nucleus in well-defined orbitals. An electron

normally does not emit light, but when it makes a transition between

two orbitals with different energies, light is emitted to conserve energy.

The lines in the emission spectra then have energies corresponding to the

energy differences between different electronic orbitals. Since there are

E=−

⎛

⎝

⎜⎜

⎞

⎠

R ⎟⎟

H nn

11

1

2

2

2

E=−

1

2

1

(^22) n
Figure 9.4A schematic diagram of the experimental arrangement for measuring the photoelectric
effect. Light strikes the metal, which is serving as the cathode, causing an electron to be emitted.
The electron is attracted by the positive electrode and the flow of electrons is measured by the
meter. By varying the strength of the electric field it is possible to determine the kinetic energy of
the emitted electrons.

CHAPTER 9 QUANTUM THEORY 181

e

hν

Required

minimum

frequency

Slope  h

Kinetic energy of

emitted electron

Frequency, ν