atomic energy levels - high energy physics

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1

Atomic energy levels

•  Exam solutions are posted. •  Problem solving sessions are

M3-5 and Tuesday 1-3 in G-140.

•  Will end early and hand back your Midterm Exam at end of class.

Announcements:

http://www.colorado.edu/physics/phys2170/

Exam 1 Results

Physics 2170 – Fall 2013 2

Average Score 36/50 => 72%


Exam 1 Comments


I graded the exam so please make an appointment and come see me, if you wish to discuss the exam as a whole or a particular problem. If you received a grade less than 25 or 50% on the exam, then you need to change your study habits.

The average score was 72% and that is a typical average score in physics. I will curve the total of the results from all sources – clicker questions, homework and exams to determine final grades.

Many people missed the decay of the Sigma particle problem, -- you will see another one the final so make sure you know how to do this!


Summary of Chapter 4 Blackbody radiation and the photoelectric effect can only be explained by a new quantum theory of light.

The quantum of light is called a photon and it has energy of E = hf = hc/λ.

Furthermore, the Compton effect shows that photons carry momentum of p = h/λ, consistent with the relativistic energy-momentum relation for massless particles which says E = |pc|.

How do we reconcile this new photon picture with all the evidence for light as a wave (interference, diffraction, etc.)?

Light is both a particle and a wave!


Light as particle and wave One modification of the two slit interference experiment is to use a light source so dim that only single photons are emitted and then watch where they land on the screen. If you mark where each photon lands on the screen, you find that they tend to land at the interference maxima even though they are only single photons!

If you add another detector which can tell which slit the photon goes through the interference pattern goes away. This is the beginning of quantum mechanics weirdness.

So the intensity of the light from the wave interference gives the probability that a given photon will land there.


Interference


If we lower the intensity of light, or the flux of photons, then we should be able to see each photon strike the screen since each photon makes a dot on the screen, but where is the interference pattern?


Interference cont.


Amazingly the interference pattern is still there, it simply takes some time for enough photons, or electrons, to strike the screen to build up a recognizable pattern Interference phenomenon still occurs even if we only let the photons, or electrons, through one at a time So what are the individual particles interfering with? Answer is apparently, themselves – light interacts with itself – amazing!


Where we are going from here The first observations that eventually lead to quantum mechanics came from light (more generally electromagnetic radiation).

Blackbody radiation, photoelectric effect, Compton effect…

We are going back to look at matter, starting with the atom

However, it turns out the real quantum mechanics behind light (Quantum Electrodynamics or QED) is well beyond the scope of this course. Feynman, Schwinger, and Tomonaga developed this in the 40s and shared the 1965 Nobel prize for it.

This will get us into non-relativistic quantum mechanics which was developed in the 1920s with Nobel prizes in the 30s.


Back to thinking about the atom

Atom

To “see” an object you need to bounce something off the object. When you use your eyes, you are using the photons which are bounced off of the object to “see” it.

For instance, if you send energetic photons (X-rays) into a body, the photons mostly go through soft tissue and scatter off the bone.

Depending on the object and the type of photons, the photons may go through (transparent) or reflect (opaque).

We are going to do this with the atom but we will be hitting it with a variety of probes (photons, electrons, and alpha particles)

γ, e, and α gun


Rutherford scattering of alpha particles off nucleus

Rutherford used alpha particles (He nuclei) to probe the atom.

Most of the atom was pretty transparent to the alpha particles.

Alpha particles that happened to go near the nucleus were scattered at large angles. Discovery of nucleus.


Atomic discharge lamps are a way of shooting electrons at an atom.

In atomic discharge lamps, lots of electrons are given significant energy (voltage). Bash into atoms. (Neon lights, Mercury street lamps, fluorescent lights)

120 Volts voltage difference or more with long tube

Shooting electrons at atoms

Moving electrons Colliding with atoms

Cathode

These free electrons excite the atomic electrons


Viewing discharge lamps with diffraction grating Using your diffraction grating •  Hold grating by the edges. Oil from your hands can fill in the

slits and ruin the grating •  Hold close to your (open) eye and look for rainbow from lights •  Rotate grating until rainbow is horizontal.

White light contains the entire spectrum.

Each atom has a unique set of colors, also called lines. The whole set is an atom’s spectrum.

Note which colors you see from the various lamps. Can also view street lights (some are sodium or mercury)


Atomic Spectra:

More complicated atoms have more lines – sun is continuous because of a mixture of many different atoms.


Given that we know light comes in photons with energy E = hc/λ, what do these atomic spectra observations imply about electrons in atoms?

Each type of atom produces unique set of colors. Discussion


Free electron hits atom

e

e

Atoms are lazy - always want to go back to lowest energy state.

e

e e

Less KE e

10ns

Ground state

Excited state Higher

energy

What does the observation of the atomic spectra tell us? •  Implies that electrons only change between very specific energies •  The only way for individual atoms to give off energy is as light •  Each time a photon is emitted an electron must be changing in

energy by that amount (releasing energy)

Step 1 Step 2 Step 3


0 (ground)

1 2 3 energy

of colliding electron


A. No light will come from the atom B. One color of light will be emitted from the atom C. Two colors of light will be emitted from the atom D. Three colors of light will be emitted from the atom E. Four or more colors of light will be emitted from the atom

Clicker question 1 Set frequency to DA

If the colliding electrons have an energy between that of level 2 and level 3 when they hit the atom then…


0 (ground)

1 2 3 energy

of colliding electron

Enough energy to excite level 2, then get 2⇒1 followed by 1⇒G, but also can go 2⇒G.


A. No light will come from the atom B. One color of light will be emitted from the atom C. Two colors of light will be emitted from the atom D. Three colors of light will be emitted from the atom E. Four or more colors of light will be emitted from the atom

Clicker question 1 Set frequency to DA

If the colliding electrons have an energy between that of level 2 and level 3 when they hit the atom then…


e e

e e e

e

For Hydrogen, transitions to ground state in ultraviolet!

No light emitted with colors in this region because no energy levels spaced with this energy.

Energy level diagrams show the energies the electrons can have.


Summary of atomic energy levels

Hydrogen

Ene

rgy

Lithium Electron energy levels in 2 different atoms …

Levels have different spacing.

Atoms with more than one electron … lower levels filled.

1) Electrons in atoms only found in specific energy levels. 2) Different set of energy levels for different atoms. 3) 1 photon emitted per electron jump down between energy

levels. Photon color determined by energy difference. 4) Electron spends very little time (10-8 s) in excited state before

hopping back down to lowest unfilled level. 5) An electron not stuck in an atom is free; can have any energy.

atomic energy levels - high energy physics

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