BioPHYSICAL chemistry

Photoelectric effect

When light of certain wavelengths strikes a metal surface, an elec-

tron is ejected from the metal in the photoelectric effect. Classically,

the kinetic energy of the ejected electron should be related to the

light intensity, or amplitude squared, and is independent of the fre-

quency used. Experimentally it is possible to measure this property

for different metals and different light conditions (Figure 9.3). It

is found that no electrons are ejected regardless of the intensity if

the light frequency is below a certain value that is characteristic

of the metal. For light above this critical frequency, the kinetic energy

is linearly dependent upon the frequency, and the intensity only

changes the number of electrons ejected (Figure 9.3).

Thus, the kinetic-energy dependence of the ejected electron

does not follow the classical prediction. Albert Einstein resolved the

discrepancy between the classical prediction and the experimental

observation in 1905. Using the same ideas as put forward by Planck,

he proposed that the light energy was not related to the amplitude

but rather was proportional to the frequency according to eqn 9.8.

A minimal energy, φ, called the work function, is required to eject

the electron from the metal. According to the conservation of energy,

the kinetic energy of the ejected electron, , is equal to the energy

of the light, hν, minus the energy required to remove the electron:

(9.14)

With this model, no electron can be ejected until the light has enough

energy to expel the electron from the metal. The critical frequency for the

photoelectric effect is when the energy of the light just matches the work

function. Above that frequency, the ejected electron will have energy that

is in excess of the energy required to leave the metal. For different metals,

the work function is different due to the different affinities of each metal for

its electrons. The slope of the increase in energy with respect to frequency

is just Planck’s constant hand is therefore the same for all metals. For

these insights, Einstein was awarded the Nobel Prize in Physics in 1921.

Atomic spectra

When objects are heated they emit light that is characteristic for each

element. Experimentally, the emitted light is observed to be not con-

tinuous but discrete (Figure 9.4). This feature suggests that the energy

associated with the atoms is discrete or quantized. In classical physics,

there is no reason for this property of quantized light emission. However,

1

2

mh^2

e^9 =−νφ

1

2

m^2

e^9

180 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

E 3

hν  E 3  E 2

E 2

E 1

Energy

hν  E 2  E 1

hν  E 3  E 1

Figure 9.3The presence of
the discrete lines in the
emission spectra of atoms
suggests that the electrons
are making transitions
between orbitals with
discrete energy levels.