# Photoelectric Effect

```- - - - Negatively
Zinc
charge Zinc - - - -
1. Negatively charge a sheet of zinc.
2. Shine long wavelength radio waves on the zinc.
3. Zinc remains negatively charged.
4. Increase intensity of radio waves…
5. Zinc remains negatively charged.
6. Change wavelength of EM radiation
7. Zinc discharges!
What’s happening?
• E-M radiation is causing the electrons to
leave the metal, making it discharge.
• These are called electrons photoelectrons.
e
e
e
- - - - Negatively
Zinc
charge Zinc - - - -
Why?
E-M waves deliver energy
If they deliver enough energy to a particular electron, that electron could use the
energy to leave the metal surface.
WAVE
THEORY
Any wave will deliver energy !
If you shine any radiation onto
the metal for long enough
eventually enough energy will
be delivered to allow electrons
to leave.
Also, if you increase the
should occur sooner.
We can only explain
not
always behave
the
photoelectric
We
these
like
a call
wave
a
effect
is
behaving
like
smooth continuous
lumps
quanta
packets
ofenergy
energy
stream of
being
delivered one
or
photons.
being
delivered to a
by one.
point.
QUANTUM
THEORY
p
What’s the energy of a photon?
E=hf
f = the frequency of the radiation
h = Planck's constant
f=c/λ
LOW ENERGY !
HIGH ENERGY !
The Rules!
Each photon only interacts with one electron.
It delivers its energy to the electron and disappears (because it is a packet of pure energy and
nothing else.)
 Electron now has extra energy.
If it has enough extra energy it can leave the metal atom.
So only photons above the threshold frequency, fo, will cause photoelectric emission.
How come more intense (brighter) radiation doesn't cause emission?
More intense radiation simply means that more packets of energy (photons) are
delivered each second.
• But the energy of each packet is unchanged.
• So if there wasn't enough energy to cause photoelectric emission, making it
brighter won't change anything.
It actually takes
energy
for
an
electron to leave
the surface of the
metal
Einstein
This energy is
the
work
function, Φ.
…Conservation of Energy Principle
Compare energy received and used by the electron at the surface:
Energy supplied to the electron = hf (energy from the photon)
Energy used by the electron:
used as work function (Φ) to escape from the surface
or
is left with the electron after it has escaped, in which case it is in the form of Ek.
Energy Supplied = Energy Consumed
hf = Φ + Ekmax
hf = Φ + Ekmax
Ekmax : only electrons on the surface (Φ= 0) will have the maximum
kinetic energy on leaving.
Electrons from deep inside which make it to the surface and still
have enough energy to escape will have used some energy getting
to the surface.
e
e
These electrons will have less energy left once they are free of the
metal and so they will have E &lt; Ekmax
e
If Ephoton = hfo (i.e. the energy of the threshold frequency photons),
only the electrons on the surface will only have enough energy to
overcome the work function and no more.
So once they have escaped they will have no energy left (Ek = zero)
 The photoelectric equation becomes:
hf0 = Φ
hf = hf0 + Φ
hf = hf0 + &frac12; mv2
Metal Plate (Emitter)
0V
e
The emitter gives out
electrons: cathode.
A
Metal Plate (Collector)
By increasing the EMF of the supply you can find the potential difference at which no
If EMF
of power
supply
= 0: Flow of electrons across the gap sets up an
electrons
are able
to cross
the gap.
electromotive force (EMF) between the plates that causes a current to
around
the rest
of the to
circuit.
At thatflow
point,
the energy
needed
cross the gap = maximum E of the electrons.
k
If the EMF is &gt; 0: the emitter becomes more positive  Electrons leaving
Work done moving a charge through a potential difference is W = QV, Q=e
it are attracted back towards it.
Only really energetic electrons can make it across2 if they don't have
eV
=
&frac12;
m
v
enough energy, they can't crossstop
the gap.
Stopping Potential
eVstop = &frac12; mv2
VS
eVstop = h(f-f0)
Vstop = (h/e)(f-f0)
f0
After that, increasing the frequency of
the photons increases the maximum
kinetic energy of the photoelectrons,
Frequency so stopping them takes a larger value
of stopping potential.
Nothing happens until you get photons with energy &gt; hf0
What happens when we change the light intensity?
Current-voltage for high intensity and low intensity light
I
VS
Voltage to turn around
most energetic electron
(stopping potential)
EMF
I
High
Low
VS
turn around
• Voltage
Same KEtoelectrons
most
energetic
electron
popping
off metal.
potential)
• (stopping
So same “stopping
potential”.
EMF
• Fewer electrons pop off metal
• Current decreases.
• Current proportional to light intensity.
Initial KE
What happens to the initial KE of the electrons as the frequency of light changes?
(Light intensity is constant)
0
Frequency of light
0
0
D
Frequency
E. something different
Frequency
Initial KE
C
Frequency
Initial KE
0
B
Initial KE
Initial KE
A
0
Frequency
There is a minimum frequency
below which the light cannot kick
out electrons…
Even if wait a long time
Initial KE
As the frequency of light increases (shorter λ) 
KE of electrons being popped off increases.
(it is a linear relationship)
0
Frequency of light
```