6. atomic and nuclear physics chapter 6.4 interactions of matter with energy
TRANSCRIPT
6. Atomic and Nuclear Physics
Chapter 6.4 Interactions of matter with energy
Heinrich Hertz first observed this photoelectric effect in 1887. This, too, was one of those handful of phenomena that
Classical Physics could not explain. Hertz had observed that, under the right conditions, when light
is shined on a metal, electrons are released.
The Photoelectric effect
Photosurface
Photoelectrons
The photoelectric effect consists on the emission of electrons from a metallic surface by absorption of light (electromagnetic radiation).
An apparatus to investigate the photoelectric effect was set by Millikan and it allowed him to determine the charge of the electron.
The Photoelectric effect
When light falls on the surface, the electrons are removed from the metal’s atoms and move towards the positive cathode completing the circuit and thus creating a current.
http://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect
Whether the photoelectric effect occurs or not depends only on: The nature of the photosurface
The Photoelectric effect
The frequency of the radiation
When the intensity of the light source increases so does the current.
Current and intensity are directly proportional
A high current can be due to: Electrons with high speed Large number of electrons being emitted
To determine what exactly happens we need to be able to determine the energy of the emitted electrons.
This is done by connecting a battery between the photosurface and the collecting plate.
The Photoelectric effect
When the battery supplies a p.d. the charge of the collecting plate will be negative.
This means that the negatively charged electrons can be stopped if a sufficiently negative p.d. is applied to the electrodes.
The Photoelectric effect
G
collecting plate
evacuated tube
light
photosurface
electron
The Photoelectric effect
The electrons leave the photosurface with a certain amount of kinetic energy – EK.
To stop the electrons we must supply a potential difference (called stopping voltage) so that:
eVs = EK
The Photoelectric effect
The stopping voltage stays the same no matter what the intensity of the light source is.
This means that: The intensity of light affects the number of electrons emitted but not their
energy The energy of the electrons depends on the nature of light: the larger the
frequency, the larger the energy of the emitted electrons and thus the larger the stopping voltage
Critical of threshold frequency
The two graphs represent the EK of
the electrons versus frequency
These graphs tell us that: there is a minimum frequency fc, called
critical or threshold frequency, such
that no electrons are emitted.
if the frequency of the light source is less
than fc then the photoelectric effect does
not occur
the threshold frequency only depends on
the nature of the photosurface
The Photoelectric effect - Observations
1. The intensity of the incident light does not affect the
energy of the emitted electrons (only their number)
2. The electron energy depends on the frequency of the
incident light, and there is a certain minimum frequency
below which no electrons are emitted.
3. Electrons are emitted with no time delay – instantaneous
effect.
The Photoelectric effect
Problem:
According to Classical Physics, the electron should be
able to absorb the energy from light waves and
accumulate it until it is enough to be emitted.
Solution:
Einstein suggested that light could be considered particles
of light, photons, packets of energy and momentum or
quanta. The energy of such quantum is give by:
E = h f
where: f is the frequency of the e-m radiation
h =6.63x10-34J (constant known as Planck constant)
The Photoelectric effect
When a photon hits a photosurface, an electron will absorb
that energy.
However, part of that energy will be used to pull the
electron from the nucleus.
That energy is called the work function and represented
by Ф.
The remaining energy will be the kinetic energy of the free
electron.
So,
Ek = hf - Ф
The Photoelectric effect
Recalling that
EK = eVs
So,
eVs = hf – Ф
that is:
ef
e
hVs
The Photoelectric effect
When a photon hits a photosurface, 3 things can happen: The energy of the photon is not enough to remove the
electron nothing happens
The energy of the photon is just enough to remove the
electron: the photon’s energy equals the ionization energy
the electron leaves the atom without any Ek
The energy of the photon is larger than the ionization
energy the electron leaves the atom with Ek
Exercise:
1. What is the work function for the photosurface (in joules)?
2. What is the energy of the “green” photoelectron?
3. What is the speed of the “green” photoelectron?
4. What is the energy of the “blue” photoelectron?
5. What is the speed of the “blue” photoelectron?
Exercise:
1. What is the work function for the photosurface (in joules)?
2. What is the energy of the “green” photoelectron?
3. What is the speed of the “green” photoelectron?
4. What is the energy of the “blue” photoelectron?
5. What is the speed of the “blue” photoelectron?
Light: wave or particle
The photon has an energy given by E = hf
But if it is considered a particle it also carries momentum
p = m v
According to Einstein
E = m c2 ↔ m = E /c2
So,
p = (E /c2) c ↔ p = E / c
p = hf /c
p = h /λ
Light: wave or particle
Light can behave as a particle and the photoelectric effect is
evidence for that fact.
But if we do Young’s double slit experiment so that make
photons of light go through the slits one at each time, the
photon will produce an interference pattern.
Somehow, even when light behaves like a particle it
conserves its wave properties.
So, we talk about wave-particle duality.
De Bröglie’s wavelength
In 1923, Louis de Bröglie suggested that if
light can behave as a particle then particles
could have a wave associated to them.Louis de Broglie
The wave-particle duality or duality of matter can be applied
to matter and energy.
All particles have a wave associated to them so that
λ = h / p
Big particles have a wavelength so small that it can’t be
measured.
But small particles, like electrons, would have a wavelength
that is possible to be measured.
The electron as a wave
To have an obstacle with this size we must look at the structure of
crystals. The typical distance between atoms in a crystal is of the order
of 10-8m. When electrons are made to pass through crystals, they do
diffract thus proving its wave nature.
To prove that the electron behaves like a wave it must have wave properties,
such diffraction. To make an electron diffract around an obstacle of size d, its
wavelength λ must be comparable to or bigger that d.
An electron of mass 9.1x10-31kg and speed of 105 m/s will have a wavelength λ
= 7.2x10-9m.
Davisson and Germer experiment
In this experiment, electrons of
kinetic energy 54eV were
directed at a surface ok nickel
where a single crystal had been
grown and were scattered by it.
Using the Bragg formula and
the known separation of the
crystal atoms allowed the
determination of the
wavelength which has then
seen to agree with the De
Broglie formula.
Structural analysis by electron diffraction