Download energy is constant value in that orbit

Particle Nature of Light
In the 19th century, James Clerk Maxwell
proposed that light acted like a wave made up
of two fields:
An electric field caused by stationary electric
charges
A magnetic field caused by moving electric
charges
1831 – 1879
Scottish Physicist and
Mathematician
It was understood that charged particles
move in an object causing it to give off
electromagnetic radiation (in the form of
heat or light)..
In the 20th century, Albert Einstein and
Max Planck rethought the whole idea of
light.
Instead of thinking of light as being a
wave, Einstein thought of it as an
energized particle called a “photon”
In this theory, when something gives off
light, it is releasing photons.
1879 - 1955
German Physicist
Einstein believed that the
amount of energy in the photons
was proportional to the
frequency of light produced
Example:
Yellow light has a frequency of
5.25 x 1014 Hz. What is the
energy of the photons?
E = hf
or
E = hc/λ
E = energy of single photon (J)
Answer:
h = Planck’s constant (6.63 x 10-34 Js)
The photons of yellow light have an
energy of 3.48 x 10-19 J or 2.18 eV
F = frequency (Hz)
1 eV (electron volt) = 1.60 x 10-19 J
C = speed of light (3 x 108 m/s)
λ = wavelength
Max Planck took Einstein’s theory a step
further. He theorized that the energy of
photons cannot exist in any amount.
Photons have discrete amounts of energy
called “quanta.”
E = nhf
or
E = nhc/λ
n = number of photons
Translation:
Other energies of yellow light have to be in
multiples of 3.48 x 10-19 J. If you have light
with 6.96 x 10-19 J of energy, that would
consist of 2 photons of light.
1858 - 1947
German Physicist
According to Einstein, these photons
not only have energy, but they have
momentum.
This is true even though photons
have no mass.
The same laws of motion (and
definition of momentum) do not apply
to things moving at the speed of light.
p=E/c
or
p=h/λ
p = momentum (kgm/s)
E = energy (J)
c = speed of light
h = Planck’s constant
λ = wavelength (m)
About 0.1 eV is required to break a “hydrogen bond” in a protein molecule.
What is the minimum frequency and maximum wavelength of a photon that
can accomplish this?
Suppose that 1 x 1019 photons are emitted every 0.25 s from a light bulb that
gives off light with a wavelength of 500 nm.
What is the momentum of one photon?
If all of the light was focused on a piece of black paper and absorbed, what
would be the force on the paper?
Photoelectric Effect
Albert Einstein discovered that
when photons are cast on a metal,
they dislodge the electrons in the
metal allowing them to leave the
surface.
This phenomenon is called the
photoelectric effect.
A photocell is an evacuated glass
chamber with a negative metal
plate on one side a positively
charged cathode on the other
When the photocell has a voltage
applied to it, electrons flow to the
plate and build up. As light is
directed on the plate, electrons
dislodge and move to the cathode
across the gap.
From a wave theory perspective, the
ejected electrons can be explained by
the electric field of the incoming light.
The electric field exerts a force on the
electrons ejecting them from the metal
with a certain kinetic energy.
Wave Theory Predictions
If the light intensity is increased
(greater amplitude), the
number of electrons ejected
and their kinetic energies
should increase because of the
greater electric field present.
The frequency of light (color)
should NOT effect the kinetic
energy.
Einstein’s experiments did NOT
support these predictions.
Einstein’s Observations
More intense light dislodged more
electrons, but those electrons did not
have more kinetic energy. They
traveled at the same speed as those
with less intense light.
Different frequencies of light caused
the dislodged electrons to move with
more kinetic energy.
Einstein’s Explanation
More intense light contains more
photons, but the photons have the
same amount of energy (discrete
quantum level of energy)
Changing the frequency changes the
amount of energy (E = hf)
For every photon that hits the metal,
an electron is dislodged and all the
energy is transferred to the electron.
The photon ceases to exist.
Since electrons are held in the atom
by attractive forces, a certain
amount of energy is needed just to
get the electron to move through the
metal. This amount of energy is
called the work function (W).
Whatever energy is left over
changes to kinetic energy causing
the electron to move away from the
metal at a given speed
Since the amount of energy given off by the photon is
E = hf
hf = KE + W
h = Planck’s Constant (6.63 x 10-34 Js)
KE = kinetic energy (J)
W = work function (J)
There is a threshold frequency (fo)
that must be attained in order for
the effect to occur. If it is not met,
electrons will not move out of the
metal across the gap.
hfo = W
As the frequency of light increases,
the speed at which the electrons
move increases.
To find out the kinetic energy of the
emitted electrons, the voltage of the
circuit can be reversed making point
C negative.
That negative terminal will slow
down the emitted electrons.
Whatever voltage causes the
emitted electrons to stop is called
the stopping voltage (V0).
We know ∆V = ∆PE/q = ∆KE/q
So
KE = qV0
KE = kinetic energy of electrons (J)
V0 = stopping voltage (V)
q = charge of electron (C)
Photocells are used to create
electricity in solar panels. Incident
sunlight creates electric current.
Drawback of solar electricity is that
it cannot be stored with great
efficiency.
Also used as switches so that
street lights turn on when it gets
dark.
Circuit Diagram
What is the kinetic energy and the speed of an electron ejected from a sodium
surface whose work function is W0 = 2.28 eV when illuminated by light of
wavelength of 410 nm?
What would be the stopping voltage of the above photocell with the
corresponding incident light?
How Photons are Created
In the early 20th century, Niels Bohr
proposed a new theory about the atom
that stated:
•A single electron moves around the
nucleus in a circular orbit known as
the ground state
Danish chemist
and physicist
1885 - 1962
energy is constant
value in that orbit
•Electrons move in orbits
because they have inertia
due to their attraction to other
atoms along with centripetal
attraction toward center
because of the positive
charge in the nucleus
•The energy of the electron is
quantized, meaning it is
restricted to a distinct,
constant value
energy is constant
value in that orbit
When an atom absorbs energy from an outside source (electric current,
heat), it can move to an orbit with a higher energy called an excited state.
higher E
lower E
n=1
n=2
current
Each orbit has a distinct quantum number (n) and a distinct
amount of energy (E). Both values increase as you move away
from the nucleus.
higher E
lower E
n=1
n=2
current
Upon arriving, it immediately returns to the ground state and releases that
same amount of energy in the form of a photon.
Bohr maintained that every energy
level had a distinct amount of
energy.
For hydrogen, the energy level can
be calculated using the formula to
the right
En = -13.6(1 / n2)
En = energy of specific level
(electron volts)
n = quantum number
He also found that the energies of other
atoms could be found by modifying the
formula to
En = -13.6(Z2/ n2)
Z = atomic number of atom
The values are negative because E = 0 is
typically defined at a point located at
infinity. At this point, no energy is needed
to remove the electron.
The energy of the ground
state expressed as a
positive number tells you
the ionization energy (the
energy needed to remove
an electron)
The energy of an emitted photon
is equal to the difference in the
energy levels that the electron
traveled between.
Eu – El = hf
Eu = Energy of upper level (eV)
El = energy of lower level (eV)
hf = E = energy of photon (eV)
Like all energy, the point that
you call E = 0 is a matter of
convention.
Typically, lower energy
levels are given negative
values.
Sometimes, the
ground state is
defined as E = 0
and higher energy
levels would have
larger values in the
positive direction
Since every atom has a unique structure, their electrons behave differently
when energized.
•Sometimes electrons absorb
energy and skip levels
•Sometimes electrons release
energy level by level
These different examples of emission are what cause different substances to
have different diffraction spectral.
Energy-level
diagram for
hydrogen
Corresponding
spectral series for
hydrogen
Determine the wavelength of light emitted when a hydrogen atom makes a
transition from the n = 6 to the n = 2 energy level according to the Bohr model.
Use the Bohr model to determine the ionization energy of the He+ ion, which has
a single electron. Also, calculate the minimum wavelength a photon must have
to cause ionization.
Compton Effect
Why is the sky blue?
It is blue because molecules in the
atmosphere collide with the incoming
light causing it to scatter.
A.H. Compton discovered that a photon
that is scattered by electrons
experiences some fundamental
changes after the collision.
American Physicist
1892 - 1962
The scattered photon has a
longer wavelength which means:
•the frequency is lower
•the energy is lower
Because the energy of the photon
has decreased, the electron that it
collided with gains energy
(conservation of energy)
The scattered photon also
changes direction causing the
electron to change direction
(conservation of momentum)
The new wavelength
of the photon is
called the Compton
wavelength.
When a patient is exposed to photons of x-ray radiation in cancer
treatments, most of the photons pass right through.
Some photons undergo Compton
scattering and leave energized
electrons in the person’s body.
These energized electrons can
effectively destroy tumors in the
person’s body
Wave Nature of Matter
Two examples of thinking “out of the box”
Einstein proposed that light (which was
understood as a wave) had particle-like
properties
Louis deBroglie theorized that all particles had
wave-like properties
In the same way that Einstein proposed
that for photons:
p=h/λ
deBroglie proposed that for particles:
λ=h/p
French Physicist
1892 - 1987
λ = deBroglie wavelength (m)
h = Planck’s constant
p = momentum of particle (kgm/s)
According to deBroglie, all particles
(large and small, bowling balls and
atoms) have waves around them.
For example, the electrons around
an atom move in a wavelike pattern
around the nucleus.
DeBroglie believed that the waves
formed by the electrons could only
move at the specific frequencies
that formed standing waves.
If an electron was to move to an
excited state, it would have to
find the frequency that would
form a new standing wave
Any frequency that didn’t form a standing
wave would cause the electron’s motion
to die out.
The frequencies of the excited states are
multiples of the ground state.
Calculate the de Broglie wavelength of a 0.20-kg ball moving with a speed of
15 m/s.
Determine the wavelength of an electron that has been accelerated through
a potential difference of 100 V.
Nuclear Physics
The nuclei of atoms are composed of
protons and neutrons.
Protons have positive charge.
Neutrons have no charge.
This group of particles are called
nucleons.
You would expect protons to repel each other because of electrostatic
forces (like charges repel). But they don’t.
Inside the nucleus are forces that are much stronger than electrostatic
forces. They are called strong nuclear forces.
Four Fundamental Forces in Nature
Strong Nuclear
Force
Found between
nucleons at short
distances
Relative strength =
Electrostatic
Found between
objects with electric
charge
Relative strength =
Found between
objects with mass
Relative strength =
Found between
nucleons in
radioactive decay
Relative strength =
Gravitational
Weak Nuclear
Force
1
10-2
10-43
10-13
The atoms of a specific element all have the same number of protons, but they
have different numbers of neutrons. These various forms are called isotopes.
Isotope notation allows us to know specifically what a nucleus contains.
Z = atomic number (number of
protons)
A = mass number (number of
nucleons)
The difference between the two
numbers is the number of
neutrons.
Most isotopes in nature are stable, but some are unstable meaning they
spontaneously decay and emit new particles. These unstable isotopes are
called radioisotopes.
Henri Becquerel discovered that
when a radioactive sample was
placed in a magnetic field, it emitted
particles that were deflected in
different directions?
Some particles deflected left
Some particles deflected right.
Some particles didn’t deflect.
French Physicist
1852 - 1908
What did he conclude?
Three Types of Radioactive Decay
Alpha Decay
Alpha decay occurs because there are too many protons in a nucleus causing
excessive repulsion.
Nucleus gets rid of a bundle of protons and neutrons called an alpha particle
(positively charged). An alpha particle is a helium nucleus made up of two
protons and two neutrons.
Example of the Alpha Decay of Radium - 226 into Radon - 222
Three Types of Radioactive Decay
Beta Decay
Beta decay occurs when there are too many neutrons in a nucleus.
Extra neutrons are changed into protons and electrons. Electrons that are
emitted in these reactions are called beta particles (negatively charged).
Example of the Beta Decay of Cesium-137 to Barium-137
Three Types of Radioactive Decay
Gamma Decay
Gamma decay occurs when an entire nucleus is in an energized state (after a
previous radioactive decay).
Energy is emitted in the form of photons that are called gamma particles. The
atom experiences no change in mass.
Example of the various ways boron – 12 decays into carbon – 12. It can
either be beta decay or a combination of beta and gamma decay.
Nuclear Fission and Chain Reactions
Nuclear energy holds what many believe to be the key to solve the mounting
energy crisis we face as a global community.
1. Most of our energy comes from
nonrenewable sources.
2. The Earth’s climate may be in a
warming period (debatable) which
many believe to be a result of the
burning of fossil fuels (also
debatable)
3. Because of #1 and possibly #2,
there is good reason to investigate
the more widespread use of nuclear
energy (despite what happened in
Japan)
1. Naturally-occuring uranium -235 is
bombarded with neutrons.
2. The uranium – 235 absorbs the neutron
to form uranium – 236 which is now in
an excited state.
3. The nucleus elongates because of the
added neutron and the extra energy
which causes the nucleons to move
faster.
4. The strong nuclear force weakens
because of the new distance between
nucleons. Electrostatic force increases
causing nucleus to split into two new
nuclei (X1 and X2)
5. What results are two fission fragments
along with a few individual neutrons.
6. These new neutrons can, in turn,
continue to bombard other uranium-235
atoms causing a chain reaction.
In a chain reaction, daughter particles and isolated neutrons are created. But mass
is NOT conserved
Mass of products does not equal mass of reactants.
Some of the mass is converted into energy
Mass Defect
Albert Einstein’s most well-known in
the area of particle physics was his
introduction of the formula
E = mc2
ΔE = Δmc2
E = energy (J)
m = mass (kg)
c = speed of light (m/s)
Since c is constant, the formula shows that mass is simply a form of energy known
as “rest energy”. In a sense, it is like potential energy.
Because “c” is so large, the formula shows that a small change in mass is
equivalent to a large change in energy.
In a nuclear reaction, the masses of the products will be less than the masses of
the reactants. This change in mass is known as the mass defect.
To calculate the mass defect, the
actual masses of the subatomic
particles have to be used.
Δm = mass of reactant particles –
mass of product particles
1 u (atomic mass unit)
= 1.66 x 10-27 kg
Either convert mass to kg and
express energy in Joules or use:
ΔE = 931.5Δm
ΔE = energy (eV)
Δm = (u)
What is the missing element X in the following fission reaction?
1
0
n+
U
235
A
92
Z
X+
90
38
1
Sr + 10 n
0
What is the mass defect of the above reaction? (find masses in Appendix B)
How much energy is produced in each collision between a neutron and a
uranium atom?