Download Radiation - Electromagnetic Waves (EMR): wave consisting of

Radiation - Electromagnetic Waves (EMR): wave
consisting of oscillating electric and magnetic
fields that move at the speed of light through
space.
Photon: a quantum of light or electromagnetic wave.
Quantum: a discrete amount of energy.
Quantized: a property of a system that occurs only in
multiples of a minimum amount.
n: integer - refers to energy levels in an atom.
Photoelectron: electrons emitted in the photoelectric
effect.
Photoelectric Effect: the emission of electrons when
electromagnetic radiation falls on an object.
Incandescent body: object that emits light because of
its high temperature.
TEXT pg 838
For 200 + years, physicists accumulated evidence for
the wave nature of light and all forms of
electromagnetic radiation.
•
Maxwell (1831 - 1879) summarized in 4 equations
everything that was known about electromagnetism
and electromagnetic waves.
•
Maxwell's main ideas:
1. Electric field lines start on a positive charge
and end on a negative charge.
2. Magnetic field lines form closed loops and do
not begin or end.
3. An electric field must exist around a changing
magnetic field.
4. A changing electric field generates a magnetic
field.
•
Maxwell correctly predicted the existence of
magnetic waves and their properties but he never
saw experimental evidence of their existence.
•
many years of experiments supported Maxwell's
ideas as well as other classical physics theories.
•
but, the world of physics was about to change.
Electric and Magnetic Fields Oscillating in Space
•
Maxwell (1860s) predicted that electric charges
moving in space during a time interval produced
magnetic fields and magnetic fields moving in space
during a time interval produced electric fields.
•
when these two are produced simultaneously by
vibrating atomic particles, the energy is
transmitted as electromagnetic waves (radiation)
across space. No medium is required.
•
electric and magnetic fields oscillating at right
angles (90o) to each other.
•
all electromagnetic radiation (light, radiowaves, xrays, etc.) have a velocity in a vacuum,
c = 3.00x108 m/s, and have frequencies and
wavelengths related by c = f λ
In the early part of the twentieth century, Einstein's
Theory of Relativity and the Quantum Theory shook
the world of physics.
Einstein's Theory of Relativity was theorized in a year
but the Quantum Theory required almost 3 decades to
unfold.
Einstein (1879 - 1955)
Quantum Theory (Modern Physics)
•
by the 1890s, scientists could not explain two
troubling phenomena by using traditional
Newtonian physics and the wave theory of
electromagnetic waves (classical physics).
1. Blackbody Radiation
•
Kirchhoff defined properties of a blackbody.
•
A blackbody is a "perfect radiator" - it will emit a
complete spectrum of electromagnetic radiation.
•
objects that normally give off no radiation (appear
black) can be made to do so by heating them. As
the energy added to them increased, the type of
radiation emitted changed. However, at a certain
temperature and frequency (ultraviolet range) the
graph and experimental data did not continue to
produce the expected results.
pg 842
•
the power radiated by a blackbody depends on its
temperature. P α T4
•
the intensity is related to the frequency.
pg 841
•
Kirchhoff needed a mathematical relationship. He
could not determine the relationship so he
challenged other scientists to come up with one.
It was very complex. When physicists applied
classical physics theories, the graph obtained was
not what was happening experimentally.
•
this discrepancy between theory and observation
was so shocking they called it the ultraviolet
catastrophe.
•
in 1900, Max Planck, did mathematically calculate
the observed spectrum of radiation ONLY if he
assumed that the vibrations of atoms could only
have specific frequencies. According to Planck,
the energy given off by atoms was E = nhf where
n: an integer; 0, 1, 2..
f: frequency of vibration of atom
h: mathematical constant
h: Planck's constant = 6.63x10-34 J/Hz or J·s
•
energy could only be specific values like hf, 2hf,
3hf, etc.
pg 843
•
what Planck was essentially saying was that energy
emitted or absorbed by atoms is QUANTIZED or
exists in packages (bundles) of energy in specific
sizes.
2. Photoelectric Effect
•
the photoelectric effect confirms the theory of
the quantization of energy. Hertz was attempting
to verify Maxwell's theories. (≈ 1887) He
assembled a circuit that generated an oscillating
current that caused sparks to jump back and forth
across a gap. He showed that the sparks were
generating electromagnetic waves by seeing sparks
forming in the gap of the receiver.
•
with this, he verified Maxwell's theories that when
the metal electrodes were exposed to ultraviolet
light, the sparks were enhanced.
•
10 years later, the electron was discovered.
Physicists suggested that the UV light had ejected
electrons from the electrodes.
•
the ejection of electrons by UV light is the
photoelectric effect.
•
Lenard was the first to perform detailed
experiments on the photelectric effect. (1902) He
designed an apparatus where electrodes were
sealed in a vacuum tube with a quartz window. (UV
light does not penetrate glass.)
pg 845
•
He wanted to determine the kinetic energy of the
photoelectrons. When the emitter was - and the
collector was +, he found that when the intensity
increased, the current increased.
•
when he switched the polarity of the emitter and
the collector, he found that when he increased the
potential difference (voltage), the current would
eventually stop.
•
the potential difference that stopped all
photoelectrons is the stopping potential.
•
his findings:
i) as the intensity of the light increases, energy
absorbed by the surface increases and the number
of photoelectrons increases. (classical physics)
more intense light more energy absorbed by
metal more electrons ejected from metal
ii) classical physics also indicates that as the
kinetic energy increases, the intensity increases.
Lenard found that the kinetic energy is not
affected by the intensity. Kinetic energy is
determined ONLY by the frequency of the light.
KE dependent on frequency not intensity
•
at roughly the same time as Planck, Einstein was
working with vacuum tubes that had positive +
(Anode) and negative - (Cathode) terminals
separated by a gap. When a source of potential
difference was applied, no current flowed. But
when one terminal had electromagnetic radiation
shone on it, a current began to flow. Current is
the result of photoelectrons being ejected from
the cathode by the radiation. The electrons travel
to the anode. This did not happen with all EMR.
•
Einstein proposed that 'photoelectrons' are only
ejected from the surface of the metal terminal if
the frequency of the EMR was above a certain
minimum level called the threshold frequency, fo.
•
brightness or intensity of EMR had nothing to do
with it, as EMR wave theory had predicted.
•
in 1905, Einstein explained the photoelectric
effect by saying EMR consisted of discrete
bundles of energy which he called photons and that
atoms would only absorb energy in these bundles.
•
Photons have an energy, KE. They either give up all
their energy or none of it.
•
the energy possessed by these photons depended
on the frequency of the EMR. E = hf
•
Einstein was the first one to indicate that light
and other EMR acted like particles.
•
kinetic energy (Ek) of electron freed by
photoelectric effect is given by:
Ek = hf - hfo
hfo is sometimes replaced by
W.
Where hf is the total energy absorbed by an
electron and hfo or W is called the work function of
the metal electrode and is the minimum energy needed
to free the most loosely held electrons from the
metal's surface.
•
very few scientists accepted Einstein's arguments
on the quantum (particle) theory of light.
pg 849
Example. What is the Ek of a photoelectron that
absorbs energy from yellow light (f = 5.17x1014
Hz) if the work function of the metal from which
the electron is ejected is 2.78x10-19 J.
Expressing extremely small amounts of energy at
the atomic level is usually done in units called
electron volts (eV).
1 eV = 1.6x10-19 J
So, answer from example:
6.4x10-20 J / 1.6x10-19 J/eV = 0.40 eV
Stopping Potential (Cut-off Potential)
•
to stop the photoelectric effect, you simply have
to apply a potential difference in the opposite
direction (cut-off potential) to balance the Ek of
released electrons.
∆E = QV
so Ek = QVo
where Vo is the cut-off potential
Photons travel at the speed of light, therefore, they
have zero rest mass.
If a photon exists – it moves at c. If it does not move
with a speed, c, it ceases to exist.
Example 1.
A helium – neon laser produced light with a frequency
of 4.7 x 1014 Hz. What is the energy of the photons
produced by this laser?
Example 2.
How many photons are emitted from a 1.50 x 10-3 W
laser each second if the frequency of the laser light is
4.75 x 1014 Hz?
P 852 # 1-4
Compton Effect - momentum of a photon (1923)
•
can something that has no mass have a momentum?
•
Compton directed high energy x-rays at thin metal
foil.
•
as well as ejected electrons, Compton detected
photons of lower frequency than x-rays.
•
Compton explained that x-ray photons had collided
(like particles).
•
momentum was conserved so photons must have a
mass-equivalence from Einstein's equation
E = mc2
E
m = 2
c
mass equivalence
•
a new way had to be used to calculate the
momentum, p, of a photon.
p =
E
E
E
v
=
c
=
c
c2
c2
But E = hf
so
hc
h
λ
p=
=
c
λ
hf = hf ' +
1
2
m
v
2
e
E photon = E photon + E electron
'
Example 1.
Calculate the momentum of a 4.00 MeV photon.
Example 2.
Calculate the momentum of an electron which was
accelerated from rest through a potential difference
of 2.10 x 103 V.
DeBroglie - wave nature of matter (mid – late
1920s)
•
it was suggested that since EMR has particle
properties (Compton) that the reverse was true
and particles had wave characteristics.
•
he determined that all particles (large or small)
had wavelengths given by
λ=
h
mv
•
for small particles such as electrons, λs are large
enough to be significant.
•
why can't we observe the λs of large objects?
Example. A 1.0 kg bowling ball is rolled at 5.0 m/s
down the alley. What is its deBroglie wavelength?
h 6.63x10−.34 J / Hz
λ=
=
= 1.3 x10−34 m
mv 1.0kg (5.0m / s )
This is such an extremely small λ that at the physical
state in which we exist, we cannot detect wave motion.
Example 1.
What is the kinetic energy of an alpha particle that
has a wavelength of 1.46 x 10-15 m?
Example 2.
Through what potential difference must an electron be
accelerated so that its wavelength is 2.75 x 10-11 m?
Wave - Particle Duality of Light
•
modern age physics accepts that light sometimes
acts as a wave and at other times acts like a
particle.
•
both matter and electromagnetic energy exhibit
some properties of waves and some properties of
particles.
•
Bohr model, emission spectra, energy levels
•
problem: only 4 visible lines appeared when
hydrogen atoms were energized. How do we
explain this as a model for an atom.
•
problem: electrons moving around a nucleus in
roughly circular or elliptical paths would feel a
centripetal force and would therefore have
centripetal acceleration. But accelerating charges
produce EMR, therefore these electrons should
continuously emit energy, slow down, and eventually
collapse into the nucleus. Obviously, this does not
happen.
Bohr's Explanation
•
laws of electromagnetism do not apply at atomic
level.
•
within an atom energy is only absorbed or emitted
when electrons change energy levels and this
energy is QUANTIZED.
•
electrons are either in lowest energy state (ground
state) or certain allowed levels (excited state).
•
to move from one level to another, electrons must
emit or absorb a photon with a certain amount of
energy (E = hf).
•
this absorbed or emitted photon had an energy
value equal to the difference between energy
levels.
hf = E excited − E ground
•
Bohr found that for the hydrogen atom, the
energy associated with a particular level was given
by:
−13.6eV
En =
n2
Where n is principle quantum number (energy level)
and energy is negative because energy is being
added to pull the electron away from the nucleus.
Example 1.
A hydrogen atom emits a line spectra showing its
electron has dropped from the 4th to 1st energy
level. What is the frequency and wavelength of
the photon that has been emitted?
Example 2.
What values of n are involved in the transition that
gives rise to the emission of a 388 nm photon from
hydrogen gas?
Example 3.
Determine the wavelength and frequency of the
fourth Balmer line (n=6 to n=2) for hydrogen.
Pg 880-884