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The Photoelectric effect
Before we begin:
voltage = work done per coulomb
ie W = QV
if an electron passes through a potential
difference and slows down, its Ek is converted
to electric potential so Ek = 1/2 mv2 = QV = eV
small amounts of energy could be measured in
eV
1 eV = 1.6x10-19J
The Photoelectric effect
BEGIN
Consider a gold leaf electroscope which is charged. If it is
exposed to ultraviolet radiation:
If it is negatively charged
If it is positively charged
the leaf falls
the leaf does not rise
Why can’t this be explained by the UV ionising the air
above the GLE?
The Photoelectric effect
The explanation is that the UV is able to dislodge the
electrons from the surface of the metal when it is negatively
charged but not when it is positively charged. So the UV is
interacting directly with the electrons in the surface of the
cap of the GLE.
This has been further investigated using this apparatus:
Quartz
window
Ultraviolet Radiation
Electrometer
e-
eeVacuum
e-
UV passes through the quartz
window and ejects electrons (called
Photoelectrons) from the negative
cathode. They travel to the positive
anode and constitute a tiny current
detected by the electrometer. The
results are inexplicable with the wave
theory of light.
Quartz
window
Ultraviolet Radiation
Electrometer
eeeVacuum
e-
1. The intensity was increased / decreased.
2. The anode voltage was decreased and then taken
negative until the photocurrent reduced to zero (this
voltage is called the stopping potential Vs).
3. Different wavelengths of UV were used.
4. Different metal surfaces were used.
1
The intensity was increased
/ decreased.
2
The anode voltage was
decreased and then taken negative
until the photocurrent reduced to
zero (this voltage is called the
stopping potential Vs).
1
Photo
current
Quartz
window
Ultraviolet Radiation
Electrometer
eeeVacuum
Results and
Explanations
Intensity
e-
1
The intensity was increased
/ decreased.
2
The anode voltage was
decreased and then taken negative
until the photocurrent reduced to
zero (this voltage is called the
stopping potential Vs).
Quartz
window
Ultraviolet Radiation
Electrometer
eeeVacuum
e-
Results and Explanations
1 and 2
Photocurrent
Increased
illumination
Vs
Anode Voltage
Quartz
window
Ultraviolet Radiation
Electrometer
3
Different wavelengths
of UV were used.
e-
4
Different metal
surfaces were used.
eeVacuum
Stopping
Potential
Vs
Frequency
e-
Wave explanation
1 Increasing the
intensity increases
the current
More waves liberate more
More photons liberate more
electrons with more energy
electrons with the same energy.
BUT they do actually have the
same energy!
Would not expect to get a Vs
2 Decreasing the
ie a stopping potential
voltage until the
anode is negative and
still current flows.
Vs is the same.
3 Decrease the
frequency / increase
the wavelength
4 Using different
metal surfaces
Particle explanation
One photon ejects one electron
so there is a max energy that an
electron can have. This
corresponds to Vs.
Enegry of a photon is less so
Would expect less electrons but
energy of an electron should be
should always get some ie would
less. Some energy used to
not expect to get a Vs anyway.
liberate electron (work function
W or ).
Might produce lower or higher The work function is different so
energies but there still shouldn’t the Ek of the electron will be
be a cut off
different and hence the Vs will
be different.
Unsatisfactory explanations
SATISFACTORY EXPLANATIONS
Einstein explained the phenomena perfectly with a few simple
assunptions as follows:
The light exists in small packets (photons) of energy E =
hf (h= planck’s constant = 6.6x10-34Js).
The photons interact with electrons on a one to one basis.
Energy is required to remove an electron from the surface of
the metal (the work function) and the amount is a function of
the metal.
The remaining energy is liberated as the Ek of the photoelectron.
so Energy of
incident
Photon
Removes
electron from
metal
Balance will
be Ek of
electron
hf = W +Ek
or
hf = W + eVs
This is Einstein’s Photoelectric Equation:
At the minimum frequency to liberate photoelectrons (f=f0
= cutoff frequency) this becomes
hf0 = W
so hf = hf0 +eVs
We can rearrange the original equation to get
h
W
Vs  f 
e
e
If we vary f, Vs will vary .
This is of the form y=mx+c such that if we plot Vs on the
y axis and f on the x axis, we will obtain a straight line of
gradient h/e and intercept on the y axis of W/e.ie if you
know e you can evaluate W and h.