DOC PREVIEW
CU-Boulder PHYS 2020 - A Little Modern Physics

This preview shows page 1-2 out of 6 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Modern Physics-1A Little Modern Physics"Modern" physics means physics discovered after 1900; i.e. twentieth-century physics.The late nineteenth century (roughly 1880 – 1900) was a time of blissful ignorance for physicists. Many physicists believed that Newton's mechanics and Maxwell's E&M could explain everything. Boy, were they wrong!Three revolutions in our understanding of the physical world occurred in the 20th century:1) Special Relativity, a theory of space and time (Einstein 1905)2) General Relativity, a theory of gravity (Einstein, 1916)3) Quantum Mechanics, a theory of the behavior of atoms (Planck, Einstein, Bohr, Heisenberg, Schrodinger, Born, Dirac, Pauli, …, 1900-1928)In 1911, Ernest Rutherford (New Zealand/Britain) did anexperiment that showed that an atom consists of a small,heavy, positively-charged nucleus, surrounded by smalllight electrons. The electrons are held in orbit around thepositive nucleus by the coulomb force (similar to a planetin orbit around the sun, held by the gravitational force).The electron has a total energy Etot = KE+PE. ClassicalE&M and Newton's mechanics predicts that the electroncan have any total energy. One can show that higherenergy corresponds to a larger radius orbit with a longer period T (lower frequency f = 1/T).But if the electron can have any total energy, it can orbit with any frequency. And the atom can then give off light of any frequency. (Recall that if a charges shakes with frequency f, it gives offlight of that same frequency f.) However, this prediction conflicts with experiment. Experimentally, it is found that atoms only give off light at certain specific frequencies. Each Last update: 1/13/2019 Dubson Phys2020 Notes, University of Colorado smaller Etotal,higher frequencylarger Etotal, lower frequencyModern Physics-2element (H, He, C, N, O, etc) emits a pattern of light at particular frequencies. The pattern of frequencies give a unique fingerprint which can be used to identify the element producing the light.In the early 20th century (roughly 1918–1928), a new theory called Quantum Mechanics, was developed to explain the behavior of atoms. Quantum mechanics predicts that only certain electron energies are allowed in an atom. Classical mechanics predicts that any energy is possible, and so the allowed energies form a continuum; quantum mechanics predicts that only certain energies are allowed and so the energies are quantized, that is, discrete. The allowed energies are labeled with a quantum number n. The quantum number n = 1 is the label for the lowest allowed energy state, called the ground state. Higher energy states (n = 2, 3, etc) are excited states. The separation between energy levels is usually about a few eV's (1 eV = 1 electron-volt = 1.6  10–19 J )Light is emitted from the atom whenthe atom makes a transition from ahigher-energy state to a lower energyLast update: 1/13/2019 Dubson Phys2020 Notes, University of Colorado n = 1n = 2n = 3orbits not allowed in heren = 1En = 2n = 3n = 4n = 1En = 2n = 3n = 4n = 1En = 2n = 3n = 4transition to lower n,light emittedlight absorbed,transition to higher nModern Physics-3state. Light is absorbed by the atom when it makes a transition from a lower-energy state to a higher-energy state.Last update: 1/13/2019 Dubson Phys2020 Notes, University of ColoradoModern Physics-4Isaac Newton (around 1700) believed that light was a particle (like a little pellet) that always travels in straight lines called rays. In 1801, the English scientist Thomas Young performed the famous "double-slit" experiment that showed that light was a wave of some kind. Around 1860, Scottish physicist James Clerk Maxwell developed a theory which showed that light is an electromagnetic wave. So Newton was wrong, right? Actually, he was partially correct.Quantum mechanics predicts that light is both a wave and a particle. It has both wave-like properties (constructive and destructive interference) and it has particle-like properties. If you look real closely, a beam of light appears to made up of a stream ofparticles called photons. The photon is the smallest possible unit oflight. You cannot have an amount of light smaller than one photon.(Yes, this is weird. Einstein was the one who first explained thephoton concept, but he was mighty unhappy about it.) The energy of a single photon is given by the formulacE h f hg= =lwhere f is the frequency of the light and h is a constant, called Planck's constant (after Max Planck, German scientist, c.1900), h = 6.64  10-34 Js. The greek letter gamma ( ) is the symbol traditionally used to indicate a photon, so the energy of a photon is written E . Another useful number to know is hc = 1240 eVnm; this allows easy conversion between the energy of aphoton in eV and its wavelength in nm.When light is absorbed or emitted byatoms, the light is almost alwaysabsorbed or emitted as a single photon.The wavelength of the light is then easilyrelated to the energy difference of theinitial and final states of the atom,according to the formulaLast update: 1/13/2019 Dubson Phys2020 Notes, University of Colorado photons are particles of lightn = 1En = 2n = 3n = 4n = 1En = 2n = 3n = 4EEemissionabsorptionEEModern Physics-5f icE E E E hgD = - = =lThis is just a statement of conservation of energy. In emission, the energy lost by the atom goes into making the photon. In absorption, the energy gained by the atom came from the energy of the absorbed photon.Example. What is the energy (in eV) of visible light? The wavelength of green light is about 550 nm (the center of the visible spectrum). Energy E = (hc) /  = (1240 eVnm)/550 nm  2.3 eV. It just so happens that the energy levels of the outermost electron in atoms are usually separated by a few eV, so transitions between energy levels in atoms usually result in visible light.Example. Can a microwave oven or a cell-phone communications antenna (both of which emit microwave radiation) cause cancer? Answer: The wavelength of microwaves is about = 10 cm = 0.1 m = 108 nm. The photon energy that this produces is E = (hc) /  = (1240 eVnm)/108 nm  10–5 eV = 0.00001 eV. Chemical bonds in molecules are a few eV. In order to cause a cancer, we must break a chemical bond in a cell. The energy of a microwave photon is about 100,000 times too small to do this. Microwaves cannot cause cancer. Among the problems solved by Quantum Mechanics, that


View Full Document

CU-Boulder PHYS 2020 - A Little Modern Physics

Documents in this Course
Magnetism

Magnetism

17 pages

Lab #4

Lab #4

3 pages

Lab 9

Lab 9

6 pages

Lab 4

Lab 4

8 pages

Load more
Download A Little Modern Physics
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view A Little Modern Physics and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view A Little Modern Physics 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?