20% of the year 1 Test
4 Sub - Topics Photoelectric Effect Bohr Theory of Atom Nuclear Transmutations Nuclear Fission/Fusion
3.01 Intro to Matter Energy Interface
Classical Physics
Galileo and Newton
(1600s - 1900s) Developed Laws of Motion, Kinematics, Dynamics, etc.
Modern Physics
(1905 – Now) Inconsistencies with Classical View led to a series of new discoveries by the likes of Einstein, Planck, etc.
Developed Relativity, Quantum Mechanics, E= mc2
Quantum Mechanics
Thus far in physics we have kept matter and energy in two separate piles.
_________________________ (also called Quantum Mechanics or Wave mechanics) is the theory of how atoms, matter and energy are all related.
Problems with Light
is light a ______________________ or a ________________________________?
Back in the day, we found that light acted as a wave. What is some of the evidence of light as a wave?
2. Can ________________________________ (Bend)
3. Can ____________________________ (Spread out past a narrow gap)
5. Has a ______________________ and a ______________________
But...there are problemswith the wave theory of light.
1. The energy of light is___________________. This means that the energy of a bundle of light has to be in discrete bundles, like ping pong balls.
2. Light has been shown to have _________________. Since light has no mass, this makes no sense.
3. Particles, like ___________________, have been shown to diffract when shone through a narrow gap.
4. Moving electrons, which orbit the nucleus, should give off ____________________. As they give off radiation, they should ______________ energy. As they ____________ energy, they should slow down, and eventually crash into the nucleus.
In short....neutral atoms should not exist, and the universe as we know it should not exist. So in short, there is something wrong with our understanding of light.
f, measured in Hertz (Hz)
λ, measured in metres (m)
3.02 Photoelectric Effect
The Photoelectric Effect
When _______________________________(light) is shone on a metal surface, it can cause electrons to be ______________ (current). This is called the photoelectric effect.
However, only certain frequencies worked. Making the light more intense (brighter) should have worked according to classical wave theory, but it did not. (Think of water waves; bigger waves have more energy)
The basic idea behind the photoelectric effect is that individual photons of light have definite ______________________amounts of energy.
If the individual photon lacks enough energy, then ____________________________________.
If an individual photon has sufficient energy, a ___________________________________ will be released. From this point on, more photons (brighter light) will release ______________ photo-electrons (higher current). Below this threshold frequency, no amount of photons of light will work.
Planck’s Equation
Where: E= ________________________ f= _________________________ h= _________________________
Ex: Find the energy of a single photon of red light with a wavelength of 750 nm.
For small energy levels we sometimes use the _______________________as a unit of energy.
1 eV = 1.602 x 10-19 J
(It is the energy gained by an electron accelerated through a voltage of 1.0 V) Ex: Express the answer from the previous example in eV.
Work Function
Einstein suggested that each metal used for the cathode has a specific minimum energy that permits electrons to be ejected from it.
This minimum energy is required to do the work of liberating the electrons. It is called the ___________________________.
This is really just a restatement of the_____________________________________.
Therefore, for the photoelectric effect to occur, the energy of the incident photon must be
greater than or equal to the work function: ______________________.
Stopping Potential
When a potential is applied to the plates of the apparatus (see below) it will prevent the electrons from being ejected. This allows us to measure the kinetic energy of the electrons ejected. This potential energy is called the _________________________. It is related to the Kinetic energy
thusly:
Ex: The stopping potential of a photo effect was detected to be 2.25 V. What is the maximum kinetic energy of the ejected photoelectrons?
Mathematically this becomes:
Where: h: _________________________ f: __________________________ Ek: _________________________ Wo: _________________________
* watch out, hf will give a unit in Joules, and the other units are typically in eV. Convert. using 1 eV = 1.6 x 10-19 J
Ex: A material with a known work function of 2.30 eV is shone with incident light from a 632 nm laser.
b) What maximum wavelength of light will cause the effect to occur?
c) If light with a wavelength of 456 nm is shone on the surface, what will be the maximum kinetic energy of the ejected photoelectrons?
Photoelectric effect graph:
HWK: Read p. 704 – 707
p. 732 # 24-26, 28 (W
ovalues on p.704)
Practice Set - Photoelectric Effect
Planck’s Equation (coupled with the universal wave equation) allow us to calculate the Energy of a
single photon (quanta) of light.
E = hf v = fλ
1. What is the energy of a single photon of electromagnetic radiation a) with a frequency of 3.4 x 107 Hz
b) with a wavelength of 550 nm
Work Function is the minimum energy required to liberate an electron from the material. If the energy of the quanta is less than this value, then there will be no electrons liberated.
2. From the data table 17.1 p. 704, calculate the maximum wavelength of EM radiation which can cause photoelectric emission in:
a) silver
b) aluminum
3. Light with a wavelength of 425 nm falls on a photoelectric surface with a work function of 2.0 eV. Will this be enough to cause the photoelectric effect?
Stopping potential is equal to the max kinetic energy of the electrons emitted divided by the charge of an electron. It is the voltage which must be applied to the photoelectric apparatus to stop the liberation of electrons. Recall that we have another equation describing kinetic energy from physics 2204.
Vstop = Ek Ek = ½ mv2
e
4. What is the stopping voltage of an electron that has 3.4 x 10-19 J of kinetic energy?
5. If an electron requires 2.85 V to stop it from being released from a surface, what is the kinetic energy of the electron if it were released?
6. Electrons are ejected from a photoelectric surface with a minimum speed of 5.20 x 106 m/s. The work
function of the surface is 3.24 eV. What is the wavelength of the incident EM radiation?
Einstein’s photoelectric equation relates the ideas of photon energy to work function and stopping potential. It is basically the law of conservation of energy. Energy of an incident photon = Energy of the liberated electrons + the Energy to release them from the surface.
hf = EK + Wo
7. When EM radiation with a wavelength of 350 nm falls on a metal, the maximum kinetic energy of the ejected electrons is 1.20 eV. What is the work function of the metal?
8. Light with a frequency of 5.0 x 1014 Hz illuminates a photo electric surface that has a work function of
2.3 x 10-19 J. What is the maximum energy of the ejected electrons?
9. What frequency of EM radiation is required to liberate electrons with max kinetic energy of 1.50 eV from a surface of pure platinum? See p. 704 Table 17.1
1a 2.25 x 10-26 J 5 4.56 x 10-19 J
1b 3.62 x 10-19 J 6 15.6 nm
2a 267 nm 7 2.35 eV
2b 290 nm 8 1.01 x 10-19 J
3 Yes, Ephoton > Wo 9 1.73 x 1015 Hz
This is mass. Why is this an issue for light?
3.03 Compton and DeBroglie
The _________________________ in a movie projector contains sodium, which has a work function (Wo) of _____________. Explain, using calculations, why the photoelectric effect does not occur when the photocell is illuminated by a light with λ = 650 nm.
Compton: Momentum and Photons
Light, as a wave, should not have _____________________, since momentum requires p = mv. However, Compton’s work showed:
_____________________________________________
_____________________________________________
_____________________________________________ Where: p= ______________________
h= ______________________ = ______________________
Also, these waves could be thought of as having ______________________, since mass and energy are equivalent.
Known as Mass Equivalence
De Broglie: Matter Waves
Built on the work of Compton by proposing that since waves can act like matter, perhaps matter can be described as a wave. All moving matter, baseballs, humans and cats named Sue, can be thought of as having a __________________, but it is so incredibly small that it is not
noticeable.
Ex: Find the wavelength of a 250 kg motorcycle moving at 52 m/s.
Assign read p. 707 – 711
in class p. 732 # 30, 32, 36 (1 pm = 1x10
-12m)
Practice Set - Compton and deBroglie
Atomic Model Handout #1 (Rutherford)
Practice Set - Compton and DeBroglie
Compton discovered the scattering effect of x-rays, a pattern which could only be explained if electromagnetic radiation had momentum.
p = h / λ
1. What is the momentum of a photon whose wavelength is 450 nm?
2. Find the speed of an electron having the same momentum as a photon having a wavelength of 0.80 nm.
DeBroglie extended Compton’s work, and said that if waves had momentum, then perhaps all matter could be treated as a wave. He uses the same equation.
3. What is the DeBroglie wavelength of an electron that has been accelerated from rest to a velocity of 4.8 x 106 m/s?
4. Calculate the DeBroglie wavelength of a 1000 kg car moving at 90 km/hr.
1 1.47 x 10-27 kg. m/s
2 9.09 x 105 m/s
3 1.52 x 10-10 m
3.04 Bohr Model of the Hydrogen Atom
Emission and Absorption Lines:
There are differences in the ____________________ observed depending on what light passes through. White light passing through a prism creates the rainbow we are familiar with. Light passing through a gas like hydrogen will create an ____________________ spectrum as certain wavelengths of the light are absorbed. Light created from a hot gas (like hydrogen) will create an ___________________________, as only certain wavelengths of light are emitted.
Bohr’s Atom
Neils Bohr explained the spectral lines observed in the emission of light from hydrogen with his ____________________________. This model is a synthesis of classical and quantum concepts.
Explain emission spectra
The idea is simple. The electrons exist at certain quantized energy levels. As an electron drops from a high energy level to a lower one it will _____________ energy in the form of a
_____________. Since these energy levels (shelves) can only exist at certain levels, the emitted wavelength of light can only exist as certain ______________________as well.
Bohr’s Radius
The radius of these different energy levels can be calculated using: Where n is: ___________________________
when n = 1 the electron has the lowest orbit, and this is called the _______________________.
Ex: What is the Bohr radius of an electron in the 3rd energy level of the Hydrogen atom?
This still doesn't explain WHY these orbitals exist only at certain radii. To understand that, it is useful to think of an electron more as a wave.
Since only certain standing waves can exist, likewise, electrons can only exist at
__________________. To imagine an electron inside this radii would be akin to imagining a standing wave that exists between the ___________________ and the ________________ resonance.
Energy of the Bohr radius:
The energy of these energy levels or orbits can be obtained from E = -13.6 eV / n2. Why negative? This is the energy required to remove an electron from that level to infinity.If the electron is removed from the _________________this is called the _______________________, so if you add __________ of energy to the electron orbiting a Hydrogen atom, you create a Hydrogen ion, H+.
Ex: How much energy is released when an e drops from n = 3 to n = 2 in the hydrogen atom?
Emitted Light:
Once we know the ________________released when an electron drops down a level, we can use Planck’s law (E = hf) to determine the _______________________of the light we see. An e dropping from n = 3 to n = 2 releases _________ of energy, which corresponds to __________ light.
If the e drops from the 5th to the 2nd energy level it emits a _________ photon, which is in the __________ region of the spectrum.
Ex: What wavelength of light is observed when an e drops from n = 3 to n = 2 in the Hydrogen atom?
Assign read p. 712 - 717
in class p. 733 # 40-42
3.05 Luminosity and Wave Particle Duality
Naturally Luminous Phenomenon
____________________ materials, whilst brighter than most materials under normal light, will glow only when illuminated with ultra violet (UVA) blacklight.
(Fluorescent strips on running gear at night.)...normal light makes them brighter, and UV light makes them glow.
__________________________ (glow in the dark watches) will "charge up" under normal visible light and emit light in darkness.
These may also be charged using ultra violet light, for brighter and often longer periods of light emission. Phosphorescent materials can ___________________________ than fluorescent.
Wave-Particle Duality
In science we use _____________to explain the unseen in terms of things that we understand. Light is not a wave and it is not a particle; it is _____________, something that we cannot model or visualize.
To understand light, we must use the particle model or the wave model, depending on the experiment to be explained, but not both.
Light as a Wave
________________________- it is almost impossible to measure a single quanta of radio waves. ___________________- Young’s double slit interference pattern
___________________- Light will bend around sharp edges.
Light as a Particle
______________________- it is hard to observe diffraction in gamma rays __________________________- “quanta” or bundles of energy
_____________________- Light has momentum
_______________________- Light from an excited gas will only display certain bright lines, not a “rainbow.”
____________________ - The predicted "Wave" results did not match the observed results. (more later)
A __________________is any object above 0° K which radiates photons of light.
The Ultraviolet catastrophe is the error at short wavelengths for the energy emitted by an ideal black-body. The error, much more pronounced for short wavelengths, is the difference between the black curve (the wrong curve predicted by the wave model) and the blue curve (the correct curve predicted by quantum mechanics).
Assign: Natural and Artificial sources of radiation
3.06 Natural and Artificial Sources of Radiation
Natural Radiation
Radiation exists all around us. ___________________is defined as the spontaneous
disintegration of atomic nuclei through the emission of radiation (electromagnetic waves) or particles.
As these heavy radioactive elements decay and emit radiation, they become a new element which is more stable. This changing of one element into another is called a ______________________.
This is not a chemical change.
Sources of Radiation:
1. Geological sources: _____________________________
2. Cosmic and Atmospheric sources: _____________________________ 3. Human-made sources: ___________________________________
U
232
92
Nuclear structure and properties:
______________: the positively charged core of the atom
______________: negatively charged particles of very little mass that inhabit energy levels or shells around the nucleus.
______________: positively charged particles in the nucleus. Much more massive than electrons. ________________: particles in the nucleus with no charge. Same mass as a proton.
________________: protons and neutrons (they are in the nucleus.)
________________: number of electrons or protons (found on periodic table, always a whole #) ____________________: number of nucleons (not found on periodic table...discuss the decimal)
Representing Elements:
We usually represent an element like this:
A X
Z Where: A: ______________________ Z: ______________________ X:______________________
The 3 of neutrons can be found from:
Example: An atom has a mass number of 59 and 28 electrons. Write the notation for this element. (see p. 805 for a periodic table)
Isotopes:
The atomic mass of silver is 107.9 instead of 109.
This is because silver is composed of two types of atoms. Some of them have 62 neutrons, while the rest have only 60 neutrons. This difference in neutrons gives an average atomic mass of 107.9.
When you have atoms of the same element which have different numbers of neutrons they are called ______________. For example, there are three isotopes of hydrogen.
a) normal hydrogen b) deuterium c) tritium
H
1 1 2 1H
3 1H
Unified Atomic Mass Units, u:
We define the mass of a neutral carbon isotope 12C to be exactly 12 u. Other particles are compared to this. To convert from kg we use:
1 u = 1.66 x 10-27 kg = 931.5 MeV/c2
Mass Defect and Mass Difference:
The mass of a stable nucleus is always _______________ the sum of its component parts. The difference between the atomic mass (in u) and the atomic number (A) is known as the
__________________.
To keep neutrons and protons stuck together requires energy. This __________________ turns directly into ____________________ which keeps the nucleus together.
This is the energy you must add to break apart a nucleus.
In decay and fission reactions, this ____________________ gets converted into energy using Einstein’s famous equation, e = mc2. (More on this later)
Ex: An isotope of Fluorine 19 has a mass of 18.9984 u. If the mass of a neutron is 1.008665 u and the mass of a proton and electron together (H) is 1.007825 u, find the mass defect for the Fluorine atom.
1. Write notation
2. Determine parts
3. Determine mass of bits
4. Find mass defect by subtracting mass of "bits" from mass of whole atom
How much energy does this represent?
HWK: Assign read p. 738 - 743 Do p. 773 36, 37, 42
Practice Set - Mass Defect and Mass Difference
Physicists use many different units for mass, given that the things they talk about are quite wee.
1 u = 1.66 x 10-27 kg = 931.5 MeV/c2
1. Complete the following table
u Kg MeV/c2
a) 0.9974 u
b) 1.48 x 10-26 kg
c) 425.2 MeV/c2
If you were to weigh the individual particles in an atom they would weigh more than the whole atom itself. As weird as this seems, the mass defect simply gets converted into the
binding energy which holds the nucleus together.
2. Calculate the mass defect for the following atoms. Given: mn = 1.008665 u
m(1H) = 1.007825 u (this includes one p+ and one e-)
a) Fluorine - 19, mass = 18.998404 amu
c) Boron - 10, mass = 10.012936 amu
The mass defect doesn’t just disappear, it gets converted into the binding energy which holds the nucleus together. We can calculate the binding energy by applying Einstein’s
famous e = mc2 to the mass defect.
3. For each of the three elements in question #2, use e = mc2 to calculate the binding energy. (Don’t forget to convert u into kg first)
1a 1.656 x 10-27 kg, 929.1 MeV/c2 3a 2.371 x 10-11 J
1b 8.910 u, 8305 MeV/c2 3b 1.689 x 10-11 J
1c 0.4546 u, 7.570 x 10-28 kg 3c 1.039 x 10-11 J
2a 0.15867 u 2b 0.11303 u 2c 0.06951 u
3.07 Natural Transmutations
Natural Transmutations
The ________________________ (the one that glues protons to protons and neutrons) is very short range.
On the other hand, the _____________________ of proton - proton repulsion acts at long range. As the nucleus of an atom gets bigger, it becomes more and more unstable (the protons tend to push themselves apart stronger than the nuclear force can hold them together). Above Z = 82, no number of neutrons can make a nucleus stable, so all atoms above Z = 82 are naturally
_________________.
There are three types of emissions from a radioactive element. (Refer to table 18.2 p. 745)
Alpha (α) particles:
two protons and two neutrons Charge = 2+
Alpha particles have the greatest ability to strip e away from their atoms (ionizing ability) because of their large mass and charge
Alpha (α) Decay:
An unstable parent nucleus emits an alpha (α) particle. For example, Uranium 238 is a unstable atom which will emit an alpha particle. What is left over after that?
β
-Decay: (Beta minus)
These unstable isotopes have too many neutrons.
As the neutron turns into a proton it emits an ___________________.
Note that the _________________________ doesn’t change. As well, there is a _____________ released to conserve______________________. This is a tiny neutral particle. We don’t worry about them for our calculations because it has zero mass and zero charge.
β
+Decay (Positron Emission):
These unstable isotopes do not have enough neutrons, so a proton decays into a neutron by giving off a ______________, which is just a positive electron.
Electron Capture and Gamma Decay (γ):
An electron is brought into the nucleus, causing a proton to change to a neutron. When this occurs a ____________________ is released.
Note that Gamma Decay can also occur without electron capture when the nucleus decays into a more stable energy arrangement.
This does not change the nuclear structure in any way.
HWK: Assign read chart p. 750 (neglect neutrinos and antineutrinos) Do p. 751 # 2 - 4
Do p. 774 #43 - 45
Practice set - Nuclear Reactions
Radioactive elements are unstable, and the nucleus will spontaneously decay. This process is called transmutation. There are four different kinds of radioactive decay that you are responsible for.
1. Identify the kind of transmutation taking place in each decay below.
In each of these transmutations, the mass of the products is less than the mass of the reactants. This mass difference gets released as the energy of the particle/radiation.
2. Given the following information, calculate the mass difference and energy released for the alpha decay of Polonium-190. (8.1368 x 10-3 u, 7.58 MeV)
Isotope Mass (amu)
Po-190 189.99506
Pb-186 185.98432
3.08 Fission and Fusion
Nuclear FissionA heavy nucleus ___________into two lighter nuclei and releases nuclear ________________. This is usually accomplished by bombarding the heavy nuclei with neutrons. In the subsequent nuclear reaction, more neutrons are released, which can cause a ___________________to occur. Sample reaction:
In order for the chain reaction to happen, the escaping neutrons must be slowed down to ensure that they collide with more nuclei.
This slowing down of neutrons is called ____________________, and usually involves a substance such as deuterium (heavy water).
The energy released can be expressed as the energy required to break the nuclear bonds. This ___________________is a measure of the strength of the force holding the nucleons together.
The mass of the products is _________________ the mass of the reactants, and this ___________________ is what provides the energy of the reaction, according to E = mc2.
Nuclear Fusion:
Two lighter nuclei _______________________to form a heavier element.
This is the main source of energy production on the sun, and releases about 4 times as much energy as a comparable fission reaction.
There must be some way to force the positive nuclei of hydrogen atoms together to form helium. In the sun this is triggered by the immense gravitational forces. In a fusion bomb, a
_____________ is used as the trigger to start the fusion reaction.
Ex 1: For the following reaction find the amount of energy liberated in a single such reaction.
1. Find the total mass of reactants and products
2. Find the mass difference
3. Convert this mass difference into energy
Hwk: Read: 754 - 760 Don’t worry about Ex 8,9,10 Do p. 760 #2
92 235 0 1 56 141 36 92 0 1
3
U
+
n
- >
Ba
+
Kr
+
n
1 2 1 3 2 4 0 1
H
+
H
- >
He
+
n
Other than natural transmutations it is possible to release the binding energy in a fission reaction (split an atom) and in a fusion reaction (combine light atoms).
1. Using the information given in the table, calculate the energy released in each reaction below: (Ans: 173 MeV) (Ans: 17.6 MeV)
3.09 Half – Life
The time it takes for one-half of the nuclei of a sample of radioactive isotope to decay by spontaneous emission is called the _______________ of the isotope.
For example: the half-life of carbon-14 is 5730 a. (a = annum = years) After this time, half of the original nuclei will be left.
At the end of two half lives, or 11 460 a, ½ x ½ will remain, or 1/4 of the original sample. See Table 18.4 p. 751 for some sample half-lives.
Mathematically, the ___________________curve can be drawn from the function:
Where: N = __________________________________
No = __________________________________
t = ___________________________________
T1/2 = _________________________________
The number of nuclei decaying per second is defined as the _________________, and is measured in___________________. This can be written as:
Where: A0 = ______________________ A = _______________________
Ex: Radon - 222 has a half-life of 3.8 days. How long does it take a sample to decay to 10% of its original activity?
3.08 Nuclear Power
CANDU
The Canadian built CANDU reactor is renowned the world over as a safe and reliable method of producing nuclear power. CANDU stands for Canadian Deuterium Uranium, signifying that it uses __________________________ as its fuel and _________________________________ (Heavy Water) as its moderator. There are three main safety features in a CANDU reactor.
Moderator Dump
The moderator is drained from the _________________________ by gravity, and gravity fed from above. There is no pump to break down. If there is ever no moderator, the reaction stops.
Cadmium Control Rods
Cadmium rods absorb _____________, slowing down the reaction. They can be inserted into the reactor to shut down the reaction.
Moderator “poison”
A _________________________ solution containing boron can be injected into the moderator which shuts down the reaction by absorbing all the free neutrons.
