6 Quarks6 leptons (electron, 3 neutrinos, two others)

Hadrons: Baryons (3 quarks) and Mesons (2)

Plus their antiparticles

Four Fundamental forces

Strong Force (gluons)Weak force (weird particles)Electromagnetic force (photons)Gravity (gravitons)

- They both have mass- They have opposite sign- If they meet, they self-annihilate and release energy

MODERN PHYSICS: IV

np+

e-

p+n

e-

Wave-Particle Duality of Light• Einstein’s theory suggests that although a

photon of light has no mass, it does possess kinetic energy.

• Einstein further predicted that a photon of light should also have momentum as follows.

p* = hf/c = h/λ

• The fact that a photon can have momentum again implies that it has particle properties.

*Momentum, p = mass x velocity

Wave-Particle Duality of Light

-

The Compton Effect (1922):

Incident Photon = X-ray

Collision

Momentump = hf/cE = hf

E = hf ’

p = hf ’/c

E = ½ mve2

p = mve

Conservation of Energy & Momentum: The energy and momentum gained by the electron equals the energy and momentum lost by the photon.

hf/c – hf ‘/c = mve

-

Particles vs. Waves (Light)• Wave Theory:

• Explained through polarization.• Explained through reflection.• Explained through diffraction & interference.• Explained through refraction.

• Particle Theory:• Explained through photoelectric emission.• Explained through the Compton effect.• Explained through reflection.• Explained through refraction.

Wavelike Behavior of Particles• The photoelectric effect and Compton scattering showed

that electromagnetic radiation has particle properties.• Could a particle behave like a wave?

– The answer is yes!

p = mv = h/λ

λ = h/mvWhere:

λ = de Broglie wavelength

Wavelike Behavior of Particles• Proof of the wavelike behavior of particles was made by

diffracting electrons off a thin crystal lattice.• The particles showed similar interference patterns to light

when passed through a diffraction grating.

Particles vs. Waves

• Physicists have demonstrated that light has both wavelike and particle characteristics that need to be considered when explaining its behavior.

• Similarly, particles – such as electrons – exhibit wavelike behavior.

Particles WavesMass Frequency

Size Wavelength

Kinetic Energy Amplitude

Momentum

Start p. 7 5/19

Earnest Rutherford (1911)“The Gold Foil Experiment”

• Bombarded gold foil with particles from the radioactive decay of uranium238.

• Most of the particles traveled through very thin gold foil without being deflected.

• Occasionally, particles would deflect, sometimes at angles > 90o (due to a coulombic repulsive force).

• Results show that the dense positive charge is centrally located in the nucleus.

• His model is know as the nuclear model and disproved Thomson’s theory.

The Gold Foil Experiment

• Rutherford's Gold Foil Experiment

wps.prenhall.comNote: The diameter of the atom was determined to be on the order of 100,000x larger than the nucleus!

Problems with the Nuclear Model

• Electrons are under constant acceleration due to centripetal force.

• If electrons are accelerating, then they must be giving off EM radiation that will cover a continuous band of wavelengths of the EM spectrum.

• If electrons are losing energy, then they would spiral into the nucleus.

Neils Bohr (1913)1. Assumed the laws of electromagnetism do not apply inside

an atom. Consequently, an orbiting electron would not lose energy even though it is accelerating.

2. Only certain orbital radii are possible for an electron, representing an energy state (mvr = nh/2).

3. Energy is emitted or absorbed when electrons change from one discrete energy level to another.

– Energy levels are consistent with Einstein’s theory on the photoelectric effect where he said that photons have discrete amount of energy (E = hf).

The Bohr Model of the Atom• Atoms have discrete energy levels associated with changes

in location of electrons within the atom.– The lowest energy level is called the “ground state” (All electrons are

in their proper orbitals).– When an atom is not in the ground state, it is considered to be in an

“excited state”.– When an electron absorbs energy from a photon of light, it can

transition to another discrete energy level if the energy of the photon is exactly equal to the difference in energy levels.

– Orbits near the nucleus have less energy than those farther out because it takes more energy to move an electron further away.

– Note: An atom is in the excited state for a very short period of time (~10-9 sec.)!

The Bohr Model of the Atom• The Bohr model of the atom is commonly called the

“planetary model”.

• Electrons travel in well defined orbits around the nucleus of the atom.

• In Bohr model, the centripetal force of the electron is offset by the electrostatic force.

Fc = mac

mv2 kq2

r r2

Einstein & Bohr’s Theories Combined (The Bohr Radius)

+

-

Fc

v= (1)

Coulomb’s Law

Fc =

Einstein & Bohr’s Theories Combined (The Bohr Radius)

• The value of r for a given energy level can be shown to be:

h2 n2

42mkq2 Z

E = KE + EPEE = ½mv2 - kq2/r = -½kq2/r (4)

• Substituting (3) into (4) yields:

22mkq4 Z2

h2 n2

• Substituting for m, k, h and q yields:

En = (-2.18 x 10-18 J)•Z2/n2 or En = (-13.6 eV)•Z2/n2

rn = n = 1, 2, 3, … (3)

+

-

Fc

v

En = (5)

AtomicNumber

The Bohr Model – Energy Level Diagram for Hydrogen

• To energize an electron from the ground state to n = , 13.6 eV of energy must be supplied.

• Energy required to remove an electron is called the ionization energy.

• Energy levels get closer together as they approach the ionization energy. Increasing

VisibleLight

www.physics.usc.edu

+

Ei

Ef

Bohr Model and Emission Spectra• Bohr’s theory for the structure of the atom took into consideration

Einstein’s theory of photons and energy as a means to explain why Hydrogen emits only four different wavelengths of visible light.

• Bohr’s model predicts that photons of energy will be emitted in the form of light when an electron transitions from a higher energy level to a lower energy level.

-

-

•Photon emitted contains a discrete amount of energy that is specific to the transition.

Ei – Ef = hf

Ei – Ef = hc/Bohr Atom and Emission of Light

Visible Spectrum of the Hydrogen Atom

• The photons of light emitted when going from any energy level to the ground state emit light in the ultraviolet region.

• The photons of light emitted when going from other energy levels to the2nd energy level will emit light in the visible lightregion.

+

n=3

n=2

n=1

n=4

n=5

Red655nm

blue green 485nm

Violet409nm

Dark Blue433nm

The Energy Levels of the Hydrogen Atom (The Well)

• In order for an electron to change from a lower energy state to a higher energy state, the incident photon must have the exact amount of energy equivalent to the difference in energy levels of the hydrogen atom.

Ephoton = Ei – Ef

• For example: an electron transitioning from the ground state (n=1) to a higher energy level (n=2) requires a photon of 10.2eV. – If the photon had only 10eV of energy or

10.5eV of energy, nothing would happen!

Per 7

Quantization of the Energy Levels of the Hydrogen Atom

Ephoton = Ei – Ef

• While an electron in a hydrogen atom transitions from n=1 to n=3 it needs a photon with exactly 12.09eV (13.60eV – 1.51eV) of energy, how will it return to the ground state?

• When transitioning back to the ground state, the electron can take one of 3 possible transitions: 3 – 1, or 3 – 2 followed by 2 – 1.– Each jump would emit a photon with an

amount of energy equal to the difference between the two energy levels.

Problems with the Bohr Planetary Model

1. The Bohr model of the atom works for Hydrogen, but not for other elements.

2. Bohr could not explain the conflict between acceleration of a charged particle (e-) and the production of EM radiation that would lead to the collapse of the atom.

Quantum Model (Heisenberg Uncertainty Principle) - 1926

• Erwin Schroedinger and Werner Heisenberg developed a theoretical framework that established a new branch of physics called quantum mechanics.

• Their theories explain the probability of determining a particle’s position and momentum at the same time.

– y=uncertainty of a particle’s position in the y-direction– py=uncertainty of the y-component of linear momentum

( )( )4y

hp y

Note: it is not possible to determine the position and momentum of an electron at the same time!

Quantum Model (Heisenberg Uncertainty Principle) - 1926

• The quantum model predicts the “probability” of finding the electron around the nucleus of a atom.

• The probability of finding an electron is its highest in a region called the electron cloud.

www.sparknotes.com

Electron Cloud

np+

e-

p+n

e-

We like to think of electrons as being in pretty “orbits”. We like to think of electrons as particles, but they also act like waves and spend part of the time inside the nucleus!

Electrons act like waves that move in specific resonant frequencies. There is a “fundamental state” (ground state) that is close to the atom.

As energy is added to the electron, it is added in discrete “chunks” – too little energy cannot be absorbed, too much energy and some of it goes into increasing the “harmonic” of the electron and some is thrown away.

Energy is quantized at the atomic level.

All of the known energy in the universe comes from the conversion of mass into energy

In stars,Fusion turns hydrogen into Helium (with several stops along the way)Fusion turns Helium into Carbon and Nitrogen and Oxygen and … Iron

- When stars run out of Helium they blow up- Spewing all the bits into space!

np+

e-

p+n

e-

Key Ideas• The Bohr model of the hydrogen atom contains electrons

which orbit the nucleus in orbits that are associated with discrete energy levels.

• Erwin Schroedinger and Werner Heisenberg developed the quantum model of the atom with the wave-particle theory.

• An electron in any state other than the ground state is said to be excited.

• When an electron transitions from an excited state to the ground state, it will emit a photon of light and vice-versa when going from the ground state to an excited state.

Key Ideas• The atom is defined as a probability cloud of electrons with a

centrally located nucleus.• The nucleus is fractionally smaller compared to the entire

atom (1/100,000th).• J.J. Thompson developed the first working model of the atom

– the plum-pudding model.• Earnest Rutherford developed the nuclear/planetary model of

the atom as a result of the gold foil experiment.• Neils Bohr further developed the planetary model of the

atom and solved many questions about the hydrogen atom.

Covered Standards:

Mon 5/7

5.3f Among other things, mass-energy and charge are conserved at all levels (from subnuclear to cosmic).

5.3g The Standard Model of Particle Physics has evolved from previous attempts to explain the nature of the atom and states that: • atomic particles are composed of subnuclear particles • the nucleus is a comglomeration of quarks which manifest themselves as protons and neutrons • each elementary particle has a corresponding antiparticle

Stress Tues 5/8: 5.3b Charge is quantized on two levels. On the atomic level, charge is restricted to multiples of the elementary charge (charge on the electron or proton). On the subnuclear level, charge appears as fractional values of the elementary charge (quarks).

5.3j The fundamental source of all energy in the universe is the conversion of mass into energy.*

Covered Standards:

Wed 5/9

5.3j The fundamental source of all energy in the universe is the conversion of mass into energy.*

5.3a States of matter and energy are restricted to discrete values (quantized). 5.3c On the atomic level, energy is emitted or absorbed in discrete packets called photons.* 5.3 Compare energy relationships within an atom’s nucleus to those outside the nucleus. i. interpret energy-level diagrams ii. correlate spectral lines with an energy-level diagram

observe and explain energy conversions in real-world situations recognize and describe conversions among different forms of energy in real or hypothetical devices such as a motor, a generator, a photocell, a battery4.1b Energy may be converted among mechanical, electromagnetic, nuclear, and thermal forms.

4.3a An oscillating system produces waves. The nature of the system determines the type of wave produced. 4.3d Mechanical waves require a material medium through which to travel. 4.3g Electromagnetic radiation exhibits wave characteristics. Electromagnetic waves can propagate through a vacuum. 4.3l Diffraction occurs when waves pass by obstacles or through openings. The wavelength of the incident wave and the size of the obstacle or opening affect how the wave spreads out.4.3 Explain variations in wavelength and frequency in terms of the source of the vibrations that produce them, e.g., molecules, electrons, and nuclear particles. iv. differentiate between transverse and longitudinal waves

5.3h Behaviors and characteristics of matter, from the microscopic to the cosmic levels, are manifestations of its atomic structure. The macroscopic characteristics of matter, such as electrical and optical properties, are the result of microscopic interactions. 5.3i The total of the fundamental interactions is responsible for the appearance and behavior of the objects in the universe.

5.3d The energy of a photon is proportional to its frequency.* 5.3e On the atomic level, energy and matter exhibit the characteristics of both waves and particles.