where h is a very small number, J · s to be precise, called Planck’s constant,
and f is the frequency of the beam of light.
Work Function and Threshold Frequency
As the wave theory correctly assumes, an electron needs to absorb a certain amount of
energy before it can fly off the sheet of metal. That this energy arrives all at once, as a
photon, rather than gradually, as a wave, explains why there is no time lapse between the
shining of the light and the liberation of electrons.
We say that every material has a given work function, , which tells us how much
energy an electron must absorb to be liberated. For a beam of light to liberate electrons,
the photons in the beam of light must have a higher energy than the work function of the
material. Because the energy of a photon depends on its frequency, low-frequency light
will not be able to liberate electrons. A liberated photoelectron flies off the surface of the
metal with a kinetic energy of:
EXAMPLE
Two beams of light, one blue and one red, shine upon a metal with a work function of 5.0
eV. The frequency of the blue light is Hz, and the frequency of the red light is
Hz. What is the energy of the electrons liberated by the two beams of light?In order to solve this problem, we should translate h from units of J · s into units of eV · s:
We know the frequencies of the beams of light, the work function of the metal, and the
value of Planck’s constant, h. Let’s see how much energy the electrons liberated by the
blue light have:
For the electrons struck by the red light:
The negative value in the sum means that , so the frequency of the red light is too
low to liberate electrons. Only electrons struck by the blue light are liberated.
The Bohr Model of the Atom
Let’s now return to our discussion of the atom. In 1913, the Danish physicist Niels Bohr
proposed a model of the atom that married Planck’s and Einstein’s development of
quantum theory with Rutherford’s discovery of the atomic nucleus, thereby bringing
quantum physics permanently into the mainstream of the physical sciences.