Physics I Quantum/Nuclear Notes
Metric Conversion:
Most of light and quantum measures wavelengths in nanometers. 1 nm = 10-9 m. and 1 m = 109 nm. Easiest to move
decimal. To go from meters to nanometers, multiply by 109. To move from nanometers to meters, multiply by 10-9.
HW #1-2
Einstein and Energy:
• Einstein showed in 1905 that Energy is mass -- mass is energy. In his words, “the mass of a body is a measure of
its energy content”.
• The most famous equation in modern science!
Energy and mass are equivalent!
E =mc2
2
E = mc applies to all mass and energy
• Energy goes into heat when it is absorbed.
• Applies to ALL kinds of energy
• In our ordinary life, the change of mass usually too
small to detect (because c is so large!)
For a 1kg mass:
• E = mc2 -----> 1 Kg x (3 x 108)2 = 9 x 1016 Joules
1 Joule = 10-17 Kg
• About 1Kg mass = entire energy output of large
power plant in one year Light transmits energy (mass) from one end of box to the other
• Nucleus of atoms is made of particles bound together
• If a large weakly bound nucleus can be broken into smaller strongly bound nuclei, energy is released
• Rest mass of nuclei converted to other forms of energy
• Einstein’s prophetic statement: “It is not impossible that with
bodies whose energy- content is variable to a high degree (e.g. with radium salts) the theory may be successfully
put to the test.”
• The Bomb: conversion of rest mass to kinetic energy:
• Chain reaction
n + U235 - > La139+ Mo95 + 2n + kinetic energy
1 gram of mass = energy released in an atomic bomb
• Result of Einstein’s Postulates: Mass and energy are equivalent!
• Completely different from Newtonian ideas!
• Now the ideas of mass and energy are unified – two things which appeared to be completely unrelated in the old
paradigm (classical physics) are the same in the new paradigm (special relativity)!
Facts:
• Nothing can go faster than the speed of light.
• The faster you go, the more massive you become!
• As the speed increases, more and more of the energy goes into increased mass and less and less into increased
velocity
• Never reach the speed of light!
• Energy and mass are equivalent: E = mc2
• Nevertheless, agrees with Newton’s formulas for small v
• Applies to ALL forms of energy and mass
• Usually too small to be detected
Diffraction and Interference
Diffraction is the spreading of a wave around the edge of a barrier or through an opening.
Monochromatic light consists of only one color or wavelength.
Polychromatic light consists of more than one color or wavelength.
Huygen’s Principle explains diffraction: ‘Each point of a wave front acts as a new source of disturbance.
Christiaan Huygens (1629 – 1695) was a Dutch mathematician who patented the first pendulum clock, laid the foundation
for mechanics, astronomy and probability.
Huygen’s Principle can be used to explain reflection and refraction.
Young’s Double Slit Interference:
Hold two of fingers very close together; there should be only the tiniest little gap between them that you can barely see
through. Look towards a light source, light a light bulb, through the gap in your fingers. In the gap between your fingers
you should see very faint gray lines that run parallel to your fingers... these are the destructive interference "dark" fringes!
FORMULA:
λ is wavelength of light
d is the distance between the slits
y is the distance from the central bright band to the first order bright line
L is the distance between the slits to the screen
As we move from shorter wavelengths (380 nm) to longer wavelengths (759 nm) the bright fringes get further apart.
As the distance between the slits increases (2.50 mm to 4.90 mm) the bright fringes get closer.
As the distance from the slits to the screen increases (from 2.00m to 4.99 m) the bright fringes get further apart.
Characteristics of Double slit diffraction:
Central bright band
Pattern spreads out as wavelength increases
Patterns spreads out as distance to screen increases
Pattern spreads out as distance between slits decreases
:
Single Slit Diffraction:
As wavelength increases (from 400 nm to 700 nm) the central peak gets wider
As the width of the aperture increases (from to 466 nm to 1260 nm) the central peak gets narrower.
Characteristics of Single Slit Interference
Central Bright band
Narrower slit produces wider central band
Larger wavelength gives wider pattern
Diffraction Gratings:
Series of many slits etched on film. Diffraction gratings (or replica gratings) separate light into component colors
through diffraction and interference. They are often used to identify the component colors of polychromatic light.
Thin Film Interference:
The color spectrum seen in a soap bubble, or any thin film, results from the interference of the reflections of the light from
the front and back surfaces of the film. The colors seen depend on the thickness of the film. The light most strongly
reflected has a wavelength such that the film thickness is an odd multiple of λ/4. Other wavelengths will suffer partial or
total destructive interference.
HW: 6-12
Quantum:
Quantum mechanics is the study of processes which occur at the atomic scale. The word ‘quantum’ is derived from the
Latin work mean BUNDLE. So, when we are studying the motion of objects that come in small bundles we are studying
quanta. These tiny bundles that we are referring to are the electrons traveling around the nucleus.
The study of microscopic world
These elements are ‘quantized’
Example: 1 cent is $0.01 or is the quantum of US currency.
Electromagnetic radiation (light) is also quantized with quantum called photos. Light is divided into integer number of
elementary packets or photons.
So, what aspect of light is quantized? Frequency and wavelength are still any value and are still continuous (NOT
QUANTIZED): c = fλ where c is the speed of light.
However, given a light of particular frequency, the total energy of the radiation is quantized with an elementary amount
(quantum) of energy E given by: E=hf (photon energy) Where Planck’s Constant is given by: h = 6.63 x 10-34 JS = 4.14 x
10-15 eVs The energy of light with frequency f must be an integer multiple of hf. In previous sections, we dealt with such
large quantities of light that individual photos were not distinguishable. Modern experiments can be done with single
photos.
Debroglie discovered that the wavelength times the momentum of an electron was always equal to Plank’s constant: h=λp
= λmv Where p was momentum
HW: 13-20
Photoelectric Effect
At the atomic scale Newtonian Mechanics cannot seem to describe the motion of particles. An electron trajectory
between two points IS NOT a perfect trajectory as Newton’s Laws predicts. Where Newton’s Laws end Quantum
Mechanics takes over….In a BIG WAY!
One of the most popular concepts concerning Quantum Mechanics is called the “ The Photoelectric Effect”. In 1905,
Albert Einstein published this theory for which he won the Nobel Prize in 1921.
The Electron Volt = ENERGY
Before we begin to discuss the photoelectric effect, we must introduce a new type of unit:
Recall:∆
Solve for W:
Since the charge on an electron is 1.6x10-19: 1ev =1.6 x 10-19J. This is a very useful unit as it shortens our calculations and
allows us to stray away from using exponents.
What is the Photoelectric Effect?
In very basic terms, it is when electrons are released from certain type of metal upon receiving
enough energy from incident light. So basically, light comes down and strikes the metal. If the
energy of the light wave is sufficient, the electron will then shoot out of the metal with some
velocity and kinetic energy.
“When light strikes a material, electrons are emitted. The radiant energy supplies the work necessary to free the electrons
from the surface.”
When short wavelength light illuminates a clean metal surface, electrons are ejected from the metal. The photoelectrons
produce a photocurrent (Current due to photons)
First Photoelectric Experiment:
Photons stopped by stopping voltage, Vstop. The kinetic energy of the most energetic photoelectrons is: Kmax = eVstop.
Kmax does NOT depend on the intensity of the light! Single photon ejects each electron.
Single photon with energy greater than the work function Φ ejects each electron.
Second Photoelectric Experiment:
Photoelectric effect does not occur if the frequency is below the cutoff
frequency f0, no matter how bright the light!
Photoelectric Fact #1:
The Light Energy (E) is in the form of quanta called photons. Since
light is an electromagnetic wave it has an oscillating electric field.
The more intense the light, the more the field oscillates. In other
words, its frequency is greater.
E = Energy and is proportional to frequency
h = constant of proportionality – Planks Constant
h – Plank’s Constant = h=6.63x10-34 Js
E=hf
Plank’s Constant is the SLOPE of an Energy vs Frequency graph.
Photoelectric Fact #2:
The frequency of radiation must be above a certain value before the energy is enough.
This minimum frequency required by the source of electromagnetic radiation to just
liberate electrons from the metal is known as the threshold frequency, fo. The
threshold frequency is the X-intercept of the Energy vs. Frequency graph!
Photoelectric Face #3:
The Work Function, Φ, is defined as the least energy that must be supplied to remove a free electron from the surface of
the metal, against the attractive forces of surrounding positive ions.
Putting it all together:
Kinetic energy can be plotted on the y axis and the frequency on the X axis. The WORK FUNCTION is the y-intercept.
The THRESHOLD FREQUENCY is the X-intercept. PLANCK’S CONSTANT is the slope of the graph.
Photoelectric Fact#4:
The MAXIMUM KINETIC ENERGY is the energy difference
between the MINIMUM AMOUNT of energy needed (WORK
FUNCTION) and the LIGHT ENERGY of the incident photon.
Bottom line: ENERGY MUST BE CONCERVED!
Photoelectric Face #5: Stopping Potential
If the voltage is TOO LARGE the electrons WILL NOT have enough energy to jump the gap. We call this VOLTAGE
point the STOPPING POTENTIAL, Vo.
If the voltage exceeds this value, no photons will be emitted no matter how intense. Therefore it appears that the voltage
has all the control over whether the photon will be emitted and thus has kinetic energy.
Energy Levels:
The atom is the building block of all matter. It has a nucleus with protons and neutrons and an
electron cloud outside of the nucleus where electrons are orbiting and moving. Depending on the
element, the amount of electrons differs as well as the amounts or orbits surrounding the atom.
To help visualize the atom think if it like a ladder. The
bottom of the ladder is called GROUND STATE where all
the electrons would like to exist. IF the energy is
ABSORBED it moves to a new rung on the ladder or
ENERGY LEVEL called an EXCITED STATE. This state is always AWAY from
the nucleus. As energy is RELEASED the electron can relax by moving to a new energy level or rung down the ladder
Yet, something interesting happens as the electron travels from energy level to energy level. If an electron is EXCITED,
that means energy is ABSORBED and therefore a PHOTON is absorbed.
If an electron is DE-EXCITED, that means energy is RELEASED and therefore a photon is released.
We call these leaps from energy level to energy level QUANTUM LEAPS. Since a PHOTON is emitted that means it
must have a certain wavelength.
Energy of the Photon:
We can calculate the ENERGY of the released or absorbed photon provided we know the initial and final state of the
electron that jumps energy levels. ∆
Energy Level Diagrams:
To represent these transitions we can construct and ENERGY LEVEL
DIAGRAM.
NOTE: It is very important to understanding that these transitions DO NOT have
to occur in a single jump! It might make TWO JUMPS to get back to ground
state. If that is the case, TWO photons will be emitted, each with a different
wavelength and energy.
EXAMPLE:
An electron releases energy as it moves back to its ground state position. As a result, photons are emitted. Calculate the
POSSIBLE wavelengths of the emitted photons?
∆
∆
6.63 10
3
6.63 10
2
6.63 10
1
3 10! "/
1.6 10 $%
4.14 10 ' "
414("
3 10! "/
1.6 10 $%
6.21 10 ' "
621("
3 10! "/
1.6 10 $%
1.243 10 * "
1243("
This sample will release two visible (Orange , Violet) and one Infrared.
HW 26-31
Spectroscopy is an optical technique by which we can IDENTIFY a material based on its emission spectrum. It is heavily
used in Astronomy and Remote Sensing. There are too many subcategories to mention here but the one you are most
familiar with are the flame tests. When an electron gets excited inside a SPECIFIC ELEMENT, the electron releases a
photon. This photon’s wavelength corresponds to the energy level jump and can be used to identify the element.
Emission Line Spectra: So basically you could look at light from any element of which the electrons emit photons. If you
look at the light with a diffraction grating the lines will appear as sharp spectral lines occurring at specific energies and
specific wavelengths. This phenomenon allows us to analyze the atmosphere of planets or galaxies by simply looking at
the light being emitted from them.
Radioactivity:
Notations: -,+
Top Number = MASS NUMBER = # protons + # neutrons. We use the letter ‘A’
Bottom Number = ATOMIC Number = # protons in nucleus. We use letter ‘Z’
/ !
%/+ has a mass number of 238 and an atomic number of 92
Nuclear Physics – Notation and Isotopes:
An Isotope is when you have the same element, yet it has a different mass. This is a result of having extra neutrons.
Since Carbon is always going to be element #6, we can write Carbon in terms of its mass instead: Carbon – 12 and Carbon
– 14.
Radioactivity occurs when and unstable nucleus releases energy and or particles:
4 Types of Radioactive Decay:
Alpha – Ejected Helium - /0
Beta – Ejected Electron 1$
Positron – Ejected Anti-Beta particle - 1$
Gamma – Ejected Energy - 112
You may also encounter protons - $$3 and neutrons- $1( being emitted as well!
Alpha Decay: Large unstable nucleus breaks into smaller more stable nucleus plus alpha particle
Applications: Smoke detectors
Beta Decay – No real applications. Did help discover the neutrino.
Positron: Isotopes under go this decay emit positrons including carbon – 11, potassium-40, nitrogen-13, oxygen-15,
fluorine-18 and iodine – 121. Uses: PET: Positron Emission Tomography is used in nuclear medicine imaging to
produce a 3D image of a functional body process.
Gamma Decay: most dangerous type of radiation because they are very penetrating. They can be used to kill living
organisms and sterile medical equipment before use. They can be used in CT Scans and radiation therapy.
Decay Rate:
The DECAY RATE is the rate a radioactive sample decays.
If a sample contains N atoms is allowed to decay for a time ∆t, there will be a change in the number of atoms: ∆N which
depends on the decay constant ,λ, for that particular material.
The ACTIVITY is ∆N/ ∆t and is measured in Becquerel (Bq) = 1 decay per second.
∆4
6 4
∆5
The number of radioactive atoms, N, remaining after a time t can be found if you know the original number of atoms in
the sample, No and the decay constant λ.
4
47
8
where e is the base of the natural logarithm and is equal to (about) 2.72.
Half Life
The second way to examine radioactivity is to look at the half life. The half-life is the time it takes for one-half of the
sample to decay.
0.693
9$:
/
Significant Nuclear Reactions – Fusion
Nuclear Fusion is the process by which multiple like-charged atomic nuclei join together to form a heavier nucleus. It is
accompanied by the release or absorption of energy. Applications: IFE – Inertial Fusion Energy
FISSION:
Nuclear fission differs from other forms of radioactive decay in that it can be harnessed and controlled via a chain
reaction. Free neutrons released by each fission event can trigger yet more events, which in turn release more neutrons
and causes more fissions. The most common nuclear fuels are 235U and 239Pu. These fuels break apart into a bimodal
range of chemical elements with atomic masses centering near 95 and 135u.
Fission Bomb: One class of nuclear weapons is the fission bomb or atomic bomb or atom bomb. It is a fission reactor
designed to release as much energy as possible as rapidly as possible before the released energy causes the reactor to
explode and the chain reaction to stop.