Page 44 - Science at the nanoscale

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RPS: PSP0007 - Science-at-Nanoscale
June 9, 2009
Brief Review of Quantum Mechanics
34
(a) Emission of the photoelectrons depends on the frequency
fof the incident light.
(b) Light with higher frequency gives rise to photoelectrons
with higher maximum kinetic energy.
(c) A more intense light source gives rise to larger number
of photoelectrons but the maximum kinetic energy of the
photoelectrons is independent on the intensity of the light
source.
(d) For each material there is a threshold frequency f o such
that no matter how intense the light may be, no photo-
electrons will be produced if the frequency of the incident
radiation is lower than this frequency.
Einstein proposed an explanation for the photoelectric effect.
He proposed that light consists of particles known as photons.
Each photon has an energy E = h f where h is the Planck’s con-
stant. The photoelectric effect can be explained by the following
equation
h f = W + E
(3.3)
k
where W refers to the energy required by an electron to escape
from a given material. W is known as the workfunction of the
material. When an electron absorbs a photon with energy hf, the
difference hf-W will appear as the kinetic energy E of the emitted
k
photoelectron. The maximum kinetic energy of the photoelectron
is given by
(3.4)
Maximum E = h f − W
k
Hence if the energy of the photon is less than W, no photo- ch03
electrons will be produced. The threshold frequency is given by
h f o = W. More intense light means many more photons, but the
energy carried by each photon is the same since it depends only
on its frequency. Hence more intense light will only produce more
photoelectrons but the maximum kinetic energy of the electrons
remains the same. The agreement between the Einstein model
and experimental observation justified Einstein’s proposal of the
energy of the electromagnetic radiation given by E = h f . In ad-
dition, by treating light as photons, Einstein also introduced the
idea of light exhibiting particle-like behaviour.