Download Ek = hf - hfo Ek = hf

Introduction to Modern Physics
a.k.a. Some stuff we've sort of figured out
these last 100+ years
Quantum Mechanics
Quantum Mechanics begins with light.
Some experiments proved beyond
the shadow of a doubt that light
was waves.
Some other experiments proved
beyond the shadow of a doubt that
light was particles.
The truth about light was obviously hidden and it wasn't until 1900 that
people began to understand that there was something very weird about the
world of the small. Something that required a complete revision of
understanding.
A brief history:
The Quantum Mechanical era commenced in 1900
when Max Planck postulated that everything is
made up of little bits he called quanta (one
quantum; two quanta). Matter had its quanta but
also the forces that kept material objects together.
Forces could only come in little steps at the time;
there was no more such a thing as infinitely small.
A Blackbody is an object that absorbs all radiation reaching it, and
blackbody radiation is radiation emitted by a blackbody. The specific
problem that puzzled Planck is represented by a glowing hot object.
https://phet.colorado.edu/sims/blackbody-spectrum/blackbody-spectrum_en.html
Max Planck theorized that the metals begin to glow because their
vibrating molecules can only vibrate at certain quantities of energy.
These vibrating particles emit packets of energy, called quanta,
which is directly proportional to its frequency.
This was the first stepping stone to a new branch of physics called
Quantum Mechanics.
Albert Einstein took matters further when he
successfully described how light interacts with
electrons but it wasn't until the 1920's that
things began to fall together and some
fundamental rules about the world of the small
where wrought almost by pure thought.
But let's work with what we know.
It is high school after all.
Wave-Particle Duality: Light
https://www.youtube.com/watch?v=wENZmBofwSw
Christiaan Huygens helpped many
others before him that light behaved
as a wave.
Huygens’ principle states that all
points on a wave front can be thought
of as new sources of spherical waves.
Huygens also claimed that light
required an invisible medium in which
to travel called the æther (or just
ether).
Newton professed that light was a particle.
His experiments proved as much, and he ... is... Newton. Who
would question him?
His light particle travels in straight lines with maximum velocity, and
have kinetic energy. Newton’s particle theory of light does not need a
medium for light to travel in. This theory accounted for the
rectilinear propagation of light.
This theory was held for many years, even though it could not be
used to explain diffraction.
Young's Double Slit Experiment.
If light does travel like a wave, then it should undergo interference.
Consider the wave interference pattern:
The light waves are too small to detect any pattern, plus most light
sources are INCOHERENT, which means out of phase, due to the
many different frequencies emitted from the Sun, candle, etc.
Young's Double Slit Experiment.
COHERENT light must be used. This means one must use
MONOCHROMATIC light, which is a single wave of light travelling in phase
with the other waves of light.
If this light is directed through a narrow slit, it will behave like a point source
If you then direct the light from the single slit to a double slit, the double slit
acts as a pair of sources of coherent, monochromatic light, which then allows
you to observe interference effects.
Young’s double-slit experiment demonstrated conclusively that light behaves
as a wave. The experiment also provided a method to measure wavelength.
Clearly particles cannot do this.
(at least not classically)
The behaviour of the tennis balls illustrates some important differences
between particles and waves.
• Particles do not show interference effects.
• Waves do show interference effects.
• Particles deliver energy in discrete quantities, that is, separate, individual
“parcels” of energy that transfer to the screen in the small area where the
particle strikes.
• Waves do not deliver energy in discrete quantities. Waves deliver their
energy continuously over time and spread out over the screen. (intensity)
Later, studies of what happens when light shines onto metal gave some very
puzzling results that the wave theory of light could not explain.
Light, at specific frequencies, when shown on metals will cause them to
emit electrons...
Light
This is puzzling, as it requires a packet of
energy in order to break the Coulombic
force and remove the electron from its
proton pair.
AND, photons have no mass!
The minimum energy required to remove a single electron from a piece of
metal is called the work function, W. This is measured in electron volts for
convenience.
Recall:
W = q·V, where q = 1electron·e, and V= 1Volt (1V)
1eV = 1.602x10-19J
These minimum amounts of energy can be
determined by applying an electric potential.
When the energy exceeds the work function
and an electron is ejected and a table of values
can be generated.
The fact that light was able to also do this was puzzling.
photoelectric effect refers to the emission, or ejection, of
electrons from the surface of a metal in response to incident light.
Light par
cles are called photons
Ephoton = hf
Photons are discrete packets of energy
Light is said to be “quan
zed”
the light must be larger than the threshold
frequency, fo
When an electron is emied aer a collision
of a photon, it is called a photoelectron.
The only way the photoelectric effect can work is if light behaves like a particle.
(Think of two pool balls colliding.)
E = hf
Where:
E is the energy (J)
f is the frequency in Hertz
h is known as Plank's constant 6.63 x 10-34 J·s (...We'll get to this later)
The unit of Joules are rarely used for a photon or photoelectron, rather, all
energies are converted into an ELECTRON VOLT (eV)
1 eV = 1.602 x 10-19 J
Thus, we will divide our final result by 1.602 x 10-19 J/eV
If the minimum amount of energy required of a photon to eject an electron is
given by its threshold frequency, then the work function is:
hf =W
o
Then any photon with f >fo will possess extra kinetic energy given by:
Ek = hf - hf
o
Ek = hf - W
Which provides a linear relationship
between kinetic energy and the
frequency.
Ek = hf - W
Kinetic energy of
outgoing photoelectron.
Energy of incoming light.
Energy needed to free the
photoelectron.
(Threshold)
Aluminum is being used in a photoelectric effect experiment. The work function
of aluminum is 6.73x10-19 J.
(a) Calculate the minimum photon energy in eV and the frequency needed to
emit electrons.
(b) Incident blue light of wavelength 450 nm is used in the experiment.
Determine whether any electrons are emitted, and if they are, determine their
maximum kinetic energy.
NO ELECTRON EJECTED
Stopping voltage
Millikan set up an experiment that
would allow him to measure the
energy of the escaping electrons
while he varied the frequency of
the incident light source. He set up
the photoelectric tube so that a
reversed voltage could be applied
across the anode and cathode
which would stop the ejected
photoelectrons from reaching the
anode.
He called the necessary voltage the cut off or stop voltage. Thus,
the electric potential established would have the same energy as
the escaping photoelectron.
Ek electron = electric potential energy
Ek = q Vstop
Millikan now had a practical way to measure the energy of the
photoelectrons by raising the voltage until the current across the tube
stopped flowing. In this way he could measure very accurate values of the
kinetic energy of the photoelectrons for different light frequencies.
If the stopping voltage in a certain photoelectric effect is 10.0 V and the
incident wavelength of the light source is 105 nm, what is the work
function of the metal surface?
Ek electron = Ephoton - W
hλ - W
qVstop = ---c
The classical theory of electromagnetic waves predicts that a light wave with
energy also carries a certain amount of momentum,
E
p = ___
c
Einstein’s quantum theory states that light energy can only be absorbed or
emitted in discrete parcels, as single photons. Each photon carries an energy,
, therefore
photon=
hf
pphoton = ___
c
so...
and f =
___
c
λ
h
pphoton = ___
λ
This momentum was proven with the Compton Effect.
Leftover energy was re-emitted
as a lower-energy x-ray photon,
much like an elastic collision.
Note: special relativity was needed.
Suppose an atomic nucleus at rest emits a gamma ray with energy
140 keV. Calculate the momentum and the wavelength of the
gamma ray.
We'll stop here for today.