Figure 30-1 An Ideal Blackbody

Figure 30-2 Blackbody Radiation

Figure 30-3 The Ultraviolet Catastrophe

Black body radiation Black body radiation can be explained by considering the radiation energy to be an integral multiple of a constant(h) times the frequency. In other words the energy is quantized. E n =nhf n=0,1,2,3,…

Photoelectric effect

Figure 30-5 The Photoelectric Effect

Photoelectric effect

Figure 30-6 The Kinetic Energy of Photoelectrons

Compton effect MC 1 and 3 page 351 (Barrons) FR 1(a), and 2 on page 354. (Barrons)

Matter waves When an x-ray photon strikes an electron, both are scattered in a way that is consistent with the law of conservation of momentum (Compton effect). This implies that the photon has a momentum even though it has no rest mass.

Matter waves When x-rays are scattered by a crystal, the resulting pattern is similar to that of scattered particles. This implies that photons can behave like particles.

Matter waves If a beam of X-rays interacts with a crystal a pattern that looks like scattered particles.

Matter waves When a beam of electrons goes through two slits, a diffraction pattern similar to the diffraction of light results. This implies that particles can have a wavelength.

Figure Creation of an Interference Pattern by Electrons Passing Through Two Slits

Matter waves

Atomic structure Rutherford’s group performed the famous gold foil experiment and found that an atom appears to be mostly empty space.

Atomic Structure

Atomic structure He proposed a “solar system” of the atom.

Atomic structure When gases at low pressures are excited, they do not produce a typical blackbody radiation curve, but rather individual lines of different colored light.

Figure 31-3 The Line Spectrum of an Atom

Figure 31-4 The Line Spectrum of Hydrogen

Atomic structure Johann Jakob Ballmer used trial and error methods to provide a simple formula that gives the wavelengths of the visible part of the hydrogen spectrum.

Atomic structure

This was the first step in developing a quantitative understanding of the hydrogen spectrum.

Bohr model He postulated that there are certain allowable orbits for an electron around the nucleus in which no loss of energy occurs.

Problems Problems 5-9 and on page 1046 in Walker.

Quantum Mechanics and Electron Configurations Review- Bohr’s model of atom and electrons  there were orbits associated with fixed energy levels that electrons could occupy around nucleus.  The lowest energy level was closest to nucleus. When all electrons were in lowest available energy levels the atom was in the “ground state”.  By absorbing energy, electron could “jump” to a higher orbit or energy level. This was called the “excited state”  When electron fell back to ground state it would emit the energy that it had absorbed as a photon.

Quantum Mechanics and Electron Configurations Bohr’s model could not predict energy levels in atoms with more than one electron.

1926- Erwin Schrödinger- used mathematics to describe the behavior of electrons in atoms. He assumed that electrons behaved like standing waves.This is called the quantum mechanical model. A standing wave is a wave that meets itself without any overlap.

Heisenberg Uncertainty Principle it is impossible to know both the precise location and the precise velocity of a subatomic particle at the same time

Quantum mechanics restricts the energy of electrons to certain levels, but unlike Bohr’s model it does not describe an exact path the electron takes around the nucleus.

Instead it predicts probabilities of finding electrons in certain regions of space (Not in outer space, but in tiny region of space around the nucleus)

The quantum mechanical model determines the energy an electron can have and how likely one is to find the electron in various locations around the nucleus

Just like the blur of the propeller, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. The cloud is more dense where the probability of finding an electron is high. The quantum mechanical model is sometimes called the charge cloud model.

The region of highest probability for each different energy level is a plot of points. The average position of the points can be shown as a spherical shell centered on the nucleus. This shell or energy level is just the average of points on a probability plot, not a path of movement of the electron. These energy levels or shells are called principal energy levels and they are numbered 1,2,3 etc…..

The number of the shell or principal energy level is called the PRINCIPAL QUANTUM NUMBER and it is represented by the symbol n The principal energy levels are the regions in space that can be occupied by an electron Every principal energy level has one or more sublevels within it The energy of each sublevel within the principal level is different

Important stuff 1.The number of sublevels in any principal level is the same as its principal quantum number n. So the first principal energy level (n = 1) has one sublevel The 2 nd principal level (n= 2) has 2 sublevels and 3 rd principal level (n=3) has 3 sublevels and so on.

Each electron in a given sublevel has the same energy The lowest sublevel in each principal level is called the s sublevel In the first principal level it is labeled the 1s sublevel In the second principal level it is the 2s sublevel

The next higher sublevel is called the p sublevel There is no p sublevel when n = 1; this first principal level has only one sublevel, the s sublevel The two sublevels of the 2’nd principal level are labeled 2s and 2p When n = 3, a third sublevel appears, called the d sublevel When n = 4, there is a 4 th sublevel labeled f.

RECAP The quantum mechanical model determines the energy an electron can have and how likely one is to find the electron in various locations around the nucleus

When a photon with an energy exactly corresponding to the difference between two energy levels is absorbed by an atom, an electron will move from the lower to the higher energy level (become excited).

When an electron moves from a higher to the energy level to a lower energy level, a photon with an energy exactly corresponding to the difference between two energy levels is emitted by the atom,

Figure 31-8 Energy-Level Diagram for the Bohr Model of Hydrogen

Figure 31-9a The Origin of Spectral Series in Hydrogen

Figure 31-9b The Origin of Spectral Series in Hydrogen

Figure 31-9c The Origin of Spectral Series in Hydrogen

Relativity Postulates of special relativity. 1.The laws of physics are the same in all inertial frames of reference. 2.The speed of light in a vacuum is the same in all inertial frames of reference independent of the motion of the source or the receiver.

Relativity All inertial frames move with constant velocity (0 acceleration) relative to one another.

Figure 29-1 Inertial Frames of Reference

Figure 29-4 The Speed of Light for Different Observers

Relativity As an object approaches the speed of light, according to the theory of special relativity time dilation occurs.

Figure 29-5 A Stationary Light Clock

Relativity

Figure 29-6 A Moving Light Clock

Relativity

General relativity – applies to accelerated frames of reference, and to gravitation.

Relativity Principle of equivalence– all physical experiments conducted in a uniform gravitational field and in an accelerated frame of reference give identical results.

Relativity According to general relativity a gravitational field will bend light. This was proven experimentally. (pages 970 and 971).

Relativity This also results in gravitational lensing. (P 971).

Relativity For a body of mass M to become a black hole its radius R must equal.

Relativity Problems 1,2,19,31,41, and 49 on pages in Walker. (Chapter 29)

Nuclear Physics The nucleus of an atom consists of protons and neutrons (nucleons). A convenient mass unit for nucleons is the atomic mass unit (u)

Nuclear Physics (p1051) 1u= x kg A proton has the mass of u A neutron has the mass of u An electron has the mass of u

Table 32-1 Numbers That Characterize a Nucleus ZAtomic number = number of protons in nucleus NNeutron number = number of neutrons in nucleus AMass number = number of nucleons in nucleus (#protons + #neutrons)

Nuclear Physics The notation used for nuclei is Where X is the symbol for the element

Nuclear Physics For example the symbol for an isotope of carbon with 6 protons and 8 neutrons in the nucleus is written

Nuclear Physics Isotopes of an element have the same number of protons but different numbers of neutrons in the nucleus.

Nuclear Physics Hydrogen Deuterium

Nuclear Physics The symbol for an alpha particle (helium nucleus) is written

Nuclear Physics Nuclear distances are typically measured in fermi (fm) 1fermi=1fm=1x m

Nuclear Physics Nuclear distances are typically measured in fermi (fm) 1fermi=1fm=1x m

Nuclear Physics The strong nuclear force holds the nuclei together. It only acts at distances of a couple of fermis or less. It counteracts the repulsive electrostatic force acting on the protons

Nuclear Physics

Nuclear binding energy All stable nuclei that contain more than one nucleon, have masses less than that of the individual nucleons added together.

Nuclear binding energy The difference in mass is due to the energy that holds the nuclei together called the “binding energy” This phenomenon is called the mass defect  m)  Einstein’s equation E=mc 2 can be used to calculate the binding energy of a nucleus from the mass defect.

Half life Radioactive isotopes decay at different rates. The decay rate is called half-life, and it is the time it takes for half of the radioactive atoms to decay (transmute) into a new nucleus. Uranium-238 has a half-life of 4.5 billion years. Some elements have a half-life of less than a second!

Half life

Nuclear Fission Fission occurs when a heavy nucleus is split into two relatively large chunks. Fission reactions are begun by shooting a neutron into the nucleus, which initiates the reaction. Large amounts of energy are released as mass converts to energy in the reaction. This is the reaction in nuclear power plants and nuclear weapons. Below is an example of a plutonium fission reaction.

Nuclear Fusion Fusion occurs when two light nuclei combine to make a new heavier and more stable nucleus. Large amounts of energy are released in the reaction. This is what happens in the sun and in thermonuclear weapons. Here is an example of fusion. Notice how one of the products of the reaction is larger than any of the originals.

Nuclear reactions - fission