Atomic & Nuclear Physics

Early Models of the Atom

• J.J Thomson– 1856-1940– 1st to discover the

existence of the negatively charged electron.

– Since all atoms are electrically neutral, Thomson developed his Plum-Pudding Model of the atom which consists of negatively charged electrons moved around inside a sphere of positive charge.

Early Models of the Atom

• Rutherford’s Gold Foil Experiment– Using the setup seen below Rutherford

accelerated alpha () particles at a thin sheet of Gold foil. Rutherford observed that most of the particles simply passed right through the foil without having their travel path affected by the charged particles.

– Observations showed that atom could not look like the Plum-Pudding model as Thomson predicted.

Early Model of the Atom

• Rutherford’s experiment showed that the atom must consist of primarily empty space with the positively charged particles in a centralized nucleus and the negatively charged particles orbiting around it.

Early Model of the Atom

• Rutherford’s Solar System Model

Early Model of the Atom

• Problems with the Rutherford Model:– The new model of the atom suggested that due the

curved paths of the electrons (centripetal acceleration) the atom would continuously be emitting light. To release this energy the electron would have to lose energy and as a result would spiral into the nucleus…NOT GOOD!!!

– The model also suggested that the light being emitted would cover the entire spectrum, due to the loss of energy

– Why is this a problem?...Well, that’s not was observations showed.

Early Model of the Atom

• Line Spectrum– Experiments showed that when gas molecules were

excited by exposing it to an electric field the gas would emit light. Contrary to the Rutherford model the gas did not emit a continuous spectrum of light but a series of very specific wavelengths.

Early Models of the Atom

• Bohr Model– In 1913 Niels Bohr (1885-1962), proposed a

model for the hydrogen atom that would combine classical mechanics and work done in quantum mechanics by Max Planck and Albert Einstein.

Quantum Theory

• Blackbody Radiation– Have you ever wondered why the coil of an

electric stove glows red or orange as its temperature increases?

– Have you ever noticed that almost all materials show the same effect when heated?

– A blackbody is a system that absorbs all light that is incident on it.

Quantum Theory

• Given the fact that a blackbody is effective at absorbing radiation it is also very effective at giving off radiation as well.– Blackbody experiment:

• Heat a blackbody to a specific temperature and measure the amount of EM radiation being emitted at a specific frequency. Repeat for different frequencies and plot the intensity versus frequency

– This experiment showed some interesting results

Quantum Theory

• Blackbody Results– The distribution of

energy in blackbody radiation is independent of the material from which the blackbody is constructed. It depends only on the temperature

Quantum Theory

• Problems with Blackbody experiments– Although observations were consistent and

the experiment was clearly understood, attempts to explain the results using classical physics failed miserably.

Quantum Theory

• Planck’s Quantum Hypotheses– Max Planck (1858-1947) was able to

construct a mathematical formula that agreed with experimental results. To actually derive the equation he needed to make a bold assumption.

• The radiation in a blackbody at the frequency f, must be an integral multiple of a constant (h) times the frequency. In other words, the energy is quantized

Quantum Theory

• Quantization of Energy

• n = 1, 2, 3, …• f = frequency• h = Planck’s constant• h = 6.63x10-34 Js

nhfE

Quantum Theory

• Problems with Planck’s theory– Although Planck’s theory of energy

quantization explained the results of blackbody radiation, Planck did not think the light in a blackbody had a quantized energy.

• Most physicists looked at light as being a wave, which can have any energy.

– Hello Uncle Albert!!!!

Quantum Theory

• The photon:– Albert Einstein took Planck’s idea of energy

quantization seriously and applied it to blackbody radiation.

– Einstein proposed that light comes in bundles of energy called, photons, that obey Planck’s quantization hypotheses, and the energy of that photon can be found by:

hfE

Quantum Theory

• Einstein’s photon model looked at a beam of light as a beam of particles each carrying the energy hf.– Therefore, if the intensity is increased keeping

the frequency the same, more photons pass a given point in a given time.

• This now begins to pose the question:– Is light a wave or a particle? Hmmmmm…

Quantum Theory

• The Photoelectric Effect– When two separated plates

are connected to a battery an electric field is established.

– When light of a high enough frequency is incident on the negative plate electrons are released, travel across the gap and are collected by the positive plate (i.e. current flows)

Quantum Theory

• Wave Theory vs. Particle Theory– Classical wave theory gave very different predictions

from Einstein’s photon theory. To begin analyzing the differences we measure the maximum kinetic energy (Kmax) of the emitted electrons.

• To do this we reverse the connection of the battery. In this configuration the electrons will be repelled by the negative plate. If the electrons have sufficient enough energy they can still bridge the gap. The voltage that prevents any electrons from bridging the gap is called the stopping potential (Vo)

oeVK max

Quantum Theory

• Wave Theory– Assume a monochromatic light source (one color)

• Maintains a constant frequency and wavelength

– Predictions:1. If the intensity is increased, the number of electrons

ejected and their maximum kinetic energy should be increased because the higher intensity means a greater electric field amplitude (i.e. greater electron energy), and the greater electric field should eject electrons with higher speed.

2. The frequency of light should not effect the kinetic energy of the ejected electrons. Only the intensity should affect Kmax

Quantum Theory

• Experimental observations found that there was a certain frequency that below which no electrons were emitted. It also showed that the intensity of the light incident on the metal had no effect on the kinetic energy of the emitted electrons. This violated the wave theory since, the intensity, based on the wave theory, is directly proportional to the energy carried.

Quantum Theory

• Photon model:– Einstein’s photon model made completely different

predictions to the wave model.

– Predictions:1. An increase in intensity of the light beam means more

photons are incident, so more electrons will be ejected; but since the energy of each photon is not changed, the maximum kinetic energy of electrons is not changed.

2. If the frequency of light is increased the maximum kinetic energy of the emitted electrons increases linearly.

3. The minimum frequency needed to emit an electron is dependent on the material that light is incident upon. This implies the existence of a “cutoff” frequency.

Quantum Theory

• Work Function ()– Einstein’s 3rd prediction implies that the atoms

in the metal need to absorb a certain energy to release one of its electrons. Since the energy a photon carries is dependent on the frequency, there is a certain minimum photon frequency required to release an electron in the metal. This minimum energy required is called the work function of the metal.

Quantum Theory

• Kinetic Energy of emitted Photoelectrons– Given the existence of the work function, the

maximum kinetic energy of an emitted photoelectron is now dependent on both the energy of the incident photons and the material it is striking. It can be found using the following expression:

hfKmax

Quantum Theory

• Support of Photon Theory:– In 1914 Robert Millikan performed a series of

experiments that showed that Einstein’s photon model accurately predicted the results of the photoelectric effect, and the wave theory fell short.

– These findings began the idea that light has both wave characteristics and particle characteristics.

Quantum Theory

• Support of Photon model– Compton Scattering

• In 1923 Arthur H. Compton performed an experiment in which he scattered short-wavelength light (x-rays) from various materials.

• He observed that the scattered light had a slightly lower frequency than the incident light. This indicated a loss of energy.

Quantum Theory

• Compton Scattering– Through his experimental observations and

using the idea that light carried particle properties, Compton applied the laws of conservation of energy and momentum and found that the energy of the photon could also be found by using its momentum and the following relationship:

pcE

Quantum Theory

• Wave-Particle Duality– Through the observations of the Photoelectric

Effect and Compton’s experiments the particle nature of light was supported.

– However, since light can be reflected, diffracted, and refracted light also shows wave characteristics.

– This dichotomy is known as wave-particle duality, in which light can be considered both a particle and a wave. CRAZY!!!!

Quantum Theory

• Wave Nature of Matter:– In 1923, Louis DeBroglie extended the

particle theory of light.– He felt through the symmetry of nature that if

light can be thought of as both a wave and particle under certain conditions, then material objects such as electrons and other material objects (i.e. particles) might also have wave properties.

Quantum Theory

• DeBroglie Wavelength– Through his ideas, DeBroglie proposed that

the wavelength of a material particle would be related to its momentum in the same way as a photon. He therefore predicted that wavelength of a particle can be found by:

p

h

Quantum Theory

• Davisson-Germer Experiment– In 1927 Clinton Davisson and Lester Germer

performed an experiment in which they scattered electrons from the surface of a metal crystal. These scattered electrons formed a diffraction pattern much like light does shown in Young’s Double-Slit experiment.

Quantum Theory

• Verification of the DeBroglie Wavelength– The diffraction pattern formed in the

Davission-Germer experiment was used to calculate the wavelength. Through their calculations they found the experimental results were in complete agreement with DeBroglie’s predictions.

– This means that the wave-particle duality does not just apply to light but also to ordinary matter.

Back to the Atomic Model

• We left our analysis of the early model’s of the atom with the model presented by Niels Bohr in 1913. Bohr’s model attempted to explain why atoms emit only very specific wavelengths of light when excited (atomic spectra).

Early Models of the Atom

• Bohr felt that Rutherford’s solar system model of the atom has some validity but classical physics predicted that the electrons would spiral into the nucleus as they lost energy (light), and as a result destroys the atom.

• In order for this model to work, Bohr realized that the new quantum theory postulated by Planck and Einstein would have to be incorporated.

Early Models of the Atom

• Bohr Postulates for the Hydrogen atom:– Postulate 1 – The force that holds the electron to the

nucleus is the Coulomb force between electrically charged bodies.

– Postulate 2 – Only certain stable, non-radiating orbits for the electron’s motion are possible. Each stable orbit represents a discrete energy state.

– Postulate 3 – Emission or absorption of light occurs when the electron makes a transition form one stable orbit to another, and the frequency of the light f is such that the difference in orbital energies equals hf.

Early Models of the Atom

• Bohr Model– Electrons are located

in specific orbital states around the nucleus that carry a discrete amount of energy

– Light is emitted when an electron drops from a higher energy level to a lower

hf

Early Models of the Atom

• Energy Level Diagrams– Each specific energy level

an electron can be found in has an associated amount of quantized energy (eV). The energy of an emitted photon carries can be found by.

lowhighphoton EEhfE

Early Models of the Atom

• Results of Bohr Model– An atom must absorb a very specific amount of

energy to have an electron jump from one energy level to another. (n=1 n=2)

– An electron in the atom must lose a specific amount of energy in order for the atom to release a photon. (n=2 n=1)

– If an atom absorbs enough energy an electron can be completely removed from the atom (i.e. ionization). This specific amount of energy is referred to as the binding energy or ionization energy.

Nuclear Physics

• Our understanding of the structure of the atom and specifically the nucleus, and our ability to harness its energy have brought significant changes to our lives…both good and bad. – Nuclear Weapons– Nuclear Power– Medicinal (radiation treatment, MRI)– Safety (smoke-detectors)

Nuclear Physics• Structure of the Nucleus:

– The nucleus as we know is built by a combination of protons and neutrons, also known as nucleons.

• Z = Atomic Number (Number of protons in the nucleus)– This is also equal to the number of electrons surrounding the

nucleus. Must keep the atom electrically neutral.

• N = Number of neutrons in the nucleus

– Each element in nature is determined by how many nucleons exist in the nucleus, mass number (A).

NZA

Nuclear Physics

• General Notation

– X = Element– Z = Atomic number– A = Mass number

• Example

• Element = Carbon• Protons = 6• Neutrons = 14 – 6 =8

XAZ

C146

Nuclear Physics

• Isotopes:– All nuclei of a given element have the same

number of protons, but they can have different numbers of neutrons.

– Nuclei with the same number of protons but different number of neutrons are referred to as isotopes.

CC 136

126

Nuclear Physics

• Atomic mass:

– Atomic Mass Unit (u)• 1u = 1.660540x10-27kg

Particle Mass (kg) Mass (MeV/c2)

Mass (u) Charge (C)

Proton 1.672623x10-27 938.28 1.007276 +1.6x10-19

Neutron 1.674929x10-27 939.57 1.008664 0

Electron 9.109390x10-31 0.511 0.0005485799 -1.6x10-19

Nuclear Physics

• Energy-Mass Equivalence– In 1905 Albert Einstein published his special

theory of relativity. Among the many other implications this theory had on the laws of physics was the fact that mass and energy we one in the same. We could create mass from energy and create energy from mass.

2mcE

Nuclear Physics

• What holds the nucleus together:– If like charges repel each other and neutrons

carry no charge…how does the nucleus hold itself together?

• The Strong Force– The strong force is short range, acting at distances

of ~10-15m (femtometers)– The strong force is an attractive force and acts

nearly equally between all nucleons.– At short distances the strong force dominates over

both electromagnetic and gravitational forces

Nuclear Physics

• Comparing the forces of Nature

Type Relative Strength (2 protons)

Range

Strong Nuclear 1 ~1fm

Electromagnetic 10-2 Infinite

Weak Nuclear 10-6 ~10-3 fm

Gravitational 10-38 infinite

Nuclear Physics

• The stability of a nucleus is based on the competition between the repulsive electrostatic forces and the attractive strong force.

• If the number of protons increases eventually the strong force is overtaken by the electrostatic force and the nucleus begins to disintegrate.

Nuclear Physics

• Radioactivity– When an unstable nucleus changes its composition

by emitting a particle of one form or another. – Process known as radioactive decay.– Three particles could be released during decay.

• Alpha Particles () – nuclei of • Beta Particles () - electrons• Positron emission – positively charged electron (antiparticle)

• Also could decay by emission of a photon – Gamma ray ()

He42

Nuclear Physics

• Alpha Decay– When a nucleus decays by giving off an

particle it loses 2 protons and 2 neutrons

– X = Parent Nucleus– Y = Daughter Nucleus

HeYX AZ

AZ

42

42

Nuclear Physics

• Energy released during alpha decay:

U23892

Nuclear Physics

Nuclear Physics

• Beta Decay– The basic process of -decay is the

conversion of a neutron to a proton and electron

– The decay of an atomic nucleus undergoing -decay is as follows

epn 11

10

eYX A

ZAZ 1

eYX A

ZAZ 1

Nuclear Physics

• Gamma () Decay– Occurs when an excited nucleus decays to a

lower energy state….Since nuclear energies are so much larger than atomic energies the photon released is of very high energy.

NN

eNC

147

*147

*147

146

Nuclear Physics

• Binding Energy– The minimum amount of energy required to

break a stable nucleus into its constituent nucleus.

Nuclear Physics

• Nuclear Fission– The process of large nuclei splitting into two

smaller nuclei– Discovered in 1939 by Otto Hahn and Fritz

Strassman, with the observation of a uranium nucleus splitting into two smaller nuclei.

– Energy released is many orders of magnitude larger that the energy released in chemical reactions.

Nuclear Physics

• Nuclear Fission– Amount of energy

released in a fission reaction is equal to the difference in the binding energies of the parent nuclei and the daughter nuclei multiplied by the number of nucleons in the parent nucleus.

• Example:

U23592

Nuclear Physics

• Chain Reactions– Occurs due to the fact that more than one

neutron is released from a fission reaction.– Starting with one fissionable nucleus…

after only 100 generations, the number of nuclei undergoing fission is 1.3x1030. If each reaction gives off 200MeV of energy the total energy released is 4.1x1019J.

• Enough energy to supply the needs of the entire U.S. for 6 months

U23592

Nuclear Physics

• Elementary Particles– The basic building blocks of all matter.– In the early part of the 20th century there were

only 3 elementary particles.• Proton, Neutron, and Electron

– Of these 3 only the electron has since remained an elementary particle. In the last half of the 20th century ~300 new particles have been discovered.

Nuclear Physics

Nuclear Physics

• Elementary Particles– Leptons

• Leptons are particles that are only affected by the weak nuclear force which is responsible for most radioactive decay.

• No internal structure to any of these particles • There are 6 leptons and all are classified as

elementary

Nuclear Physics

Particle Symbol Antiparticle symbol

Rest Energy (MeV)

Lifetime (s)

Electron 0.511 Stable

Muon 105.7 2.2x10-6

Tau 1784 10-13

Electron Neutrino

~0 Stable

Muon Neutrino

~0 Stable

Tau Neutrino

~0 Stable

or e

e

or e

e

• Leptons

Nuclear Physics

• Hadrons– Particles that experience the weak, strong, and

gravitational forces– All Hadrons have finite mass and internal structure– Most common:

• Proton• Neutron• Hundreds of Hadrons exist in Nature

– Two subcategories of Hadrons• Mesons• Baryons

Nuclear Physics

• Mesons– Hadron formed form the combination of two

quarks

• Bayrons– Hadron formed from the combination of three

quarks

Nuclear Physics

• Quarks– To account for the internal structure observed in all

hadrons, Murray Gell-Mann and George Zweig independently proposed in 1963 the existence of truly elementary particles in which Gell-Mann called quarks

– Originally there were three quarks• Up (u)• Down (d)• Strange (s)

– In 1974 due to the discovery of large hadrons 3 more quarks have been added

• Charmed (c) • Top (c) (a.k.a. Truth)• Bottom (b) (a.k.a. Beauty)

Nuclear Physics

Nuclear Physics

• Standard Model of Atom