Physical Chemistry , 1st ed.

Solution

Calculating the energy of the light:

E(6.626 

10 ^34 Js)(4.77 

1015 s^1 )

E3.16 

10 ^18 J

Using Einstein’s equation for the photoelectric effect and substituting:

h ^12 mv^2

3.16 

10 ^18 J (2.90eV)(1.602 

10 ^19 J/eV) ^12 (9.109 

10 ^31 kg)v^2

3.16 

10 ^18 J 4.646 

10 ^19 J (4.555 

10 ^31 kg)v^2

v^2 5.92 

1012 m^2 /s^2

v2.43 

106 m/s

Verify that the units do work out to units of velocity, m/s. This velocity is

about 1% of the speed of light.

This independent experimental support of Planck’s radiation distribution
(and Einstein’s application of it to light) was not lost on the scientific com-
munity, and since 1905 this has been generally accepted as the correct under-
standing of light. Planck’s and Einstein’s work reintroduced the idea that light
can be treated as a particle—a particle having a certain amount of energy.
There was no denying the fact that light acts like a wave. It reflects, refracts, in-
terferes as only a wave can. But there can also be no denying that light has par-
ticle properties. Light can be treated as a stream of individual particles, each of
which carries a certain amount of energy whose value is determined by its
wavelength.
More proof of the particle nature of light came in 1923 when Arthur
Compton showed that the scattering ofmonochromatic(same-wavelength; lit-
erally, “same-color”) X rays by graphite caused some of the X rays to shift to a
slightly longer wavelength. The only way to account for this was to assume that
the monochromatic X rays acted as a particle with a specific energy, and that
the collision of a particle of light with an electron caused energy to be trans-
ferred between the two particles, lessening the energy of the light particle and
therefore increasing its wavelength. (There were also momentum considera-
tions, as we will see later.) In 1926, G. N. Lewis proposed the word photonas
the name for a particle of light.
The value ofhis approximately 6.626
10 ^34 Js. The unit ofh, joules
times seconds, is necessary so that when his multiplied by a frequency, which
has units of s^1 , the product yields the unit of joules, which is a unit of en-
ergy. (Other values ofhare used that have different units, but the idea is the
same.) The numerical value ofhis extremely small: on the order of 10^34 .The
implication is that one will not even notice the packaging of energy into quanta
unless one is looking at the behavior of extremely small objects, like atoms and
molecules and photons. It wasn’t until the late 1800s that science developed the
tools (like spectroscopes) to do that, so it wasn’t until then that scientists no-
ticed the difference between discrete bundles of energy and so-called continu-
ous energy.
Finally, the units ofh, joulesecond (or Js), is a combination of energy and

9.8 Quantum Theory 261