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Lecture 10: Atomic Structure
PHYS 2130: Modern PhysicsProf. Ethan Neil
(image credit: http://sciencing.com/make-3d-model-sodium-5646441.html)
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
A new lecture style• I’m trying out slides instead of a pure chalkboard
lecture today
• (My style is usually chalkboard-only, but this class is less math derivation-heavy than others I’ve taught recently.)
• My greatest concern with slides is the possibility of going too fast - please ask questions to slow me down if I do!
• Feedback welcome (this is your class.)
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PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
Announcements/reminders• Homework #4 assigned, due Wednesday 9/27 - check D2L. (The
exam will be very similar, hint hint…)
• If you need exam accommodations, make sure I have a letter
• Optional recitation/problem session: Thursdays 5-6PM, G125, led by TAs Josh Carr and Dahyeon Lee. Bring paper+something to write with!
• Other TAs can be found in the Physics Help Room (G2B90): (all times are AM)
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- Xu Zheng: Mon 9-10, Wed 9-10, Thu 10-11 - Jose Valencia: Tu/Thu 11-noon, Wed 10-11 - Hanna Lyle: Mon 10-noon, Fri 10-11
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
Atomic Structure, continued• Early experiments —> atoms contain electrons
• Atoms are neutral, so they must have some positive charge…but can’t knock anything like a positive electron out.
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“plum pudding” (or “chocolate chip”?) model
• How can we probe the internal structure of atoms?
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 5
We can do a scattering experiment! Test charges sent through atom, see where they end up.
Classical analogy: what’s inside an opaque ball of jello?
Scattering experiment: fire rubber bullets into the jello. They will bounce off any internal structures.
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 6
One possibility: small, hard core and no other internal structure.
Most bullets just go straight through, but a handful are reflected at big angles, sometimes straight back at us!
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 7
(image credit: https://commons.wikimedia.org/wiki/File:Geiger-Marsden_experiment.svg)
Rutherford experiment: same basic idea. Shoot gold atoms with alpha particles (He++ ions)
Of course, we can’t line our shots up with a single atom - look for overall results from many alphas.
“It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it
came back and hit you.” - E. Rutherford
?
?
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 8
(which element is this?)
Modern picture: nucleus is not fundamental, made of two nucleons: protons (p, electric charge +e) and
neutrons (n, charge 0.) About the same mass:
# protons = Z = “atomic number” # neutrons = N
# nucleons = Z+N = A = “mass number”
Periodic table organized by Z. Same Z, different A —> “isotopes”.
Strong nuclear force binds p/n (otherwise, protons repel and
nucleus is blasted apart!) More on nuclear forces later.
mn ⇡ mp ⇡ 2000⇥me
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 9
p p
p p n n n
n p
10-14 m
10-10 m
Deviations from expected electric-force scattering were eventually seen, somewhat later on (in aluminum.)
Use conservation of energy to estimate nuclear size (HW) - roughly 10-14 m!
Lots of empty space! If nucleus were 50’ wide (Gamow tower)…
…edge of atom would be 100 miles (reaches to Wyoming)
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
Rutherford’s “solar system” model
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• Still the “modern picture”, in terms of how charge is distributed.
• Rutherford model: a ‘solar system’ of electrons in calm, circular orbits around nucleus.
• Coulomb force acts like gravity:
Fe =kq1q2r2
vs.
Fg =Gm1m2
r2
But there are two big problems!
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
CQ: In the Rutherford model, an electron moves to an orbit further from the nucleus.
How does its total energy E change?How does its electrostatic potential U change?
• A. E up, U down
• B. E down, U down
• C. E up, U up
• D. E down, U up
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PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 12
This force gets weaker as the electron moves away from the nucleus (1/r2.)
But pulling it away is working against the force, so U must be negative and
increasing.
U =k(+Ze)(�e)
r< 0
ETO ← • e-
u^
#Force is attractive between opposite charges:
~Fe =kq1q2r2
=�kZe2
r2ETO ← • e-
u^
#
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
First problem: “death spiral”
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• Any object in a circular orbit is accelerating constantly
• From Maxwell’s equations, accelerating charges generate light
• Light carries energy!
• So the electron should slowly radiate its orbital energy away (E and U decrease), falling in to the nucleus.
—> predict atoms are unstable!
How unstable? You can calculate the lifetime of an atom in this model, and you get about 10-11 seconds (!)
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
Second problem: emission of light
• Suppose that for some reason, the death spiral doesn’t happen - maybe there electrons stop at some minimum energy (the “ground state”).
• We still expect electrons to be allowed in any orbit outside of that minimum. (Again, like solar system: planets exist in specific orbits, but they could have been anywhere.)
• Those electrons with extra energy can still emit light (a photon, E=hf) and go back to the ground state.
• Continuous energy differences —> continuous spectrum of light predicted.
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¢allowed orbits ?
,
- -
,
'
"+0-1.41 rmin? '
\/
--
-
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
The discharge lamp• To see light emission from atoms, pump energy into them to put orbital
electrons in excited (higher-E) states
• Discharge lamp: accelerate electrons, bash them into atoms. Recoil knocks atomic electrons into higher orbits.
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120Voltsvoltagedifferenceormorewithlongtube
Moving electrons Colliding with atoms
Cathode(hotwire)
Anode(plate)
(sta>onary)Atoms
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 16
(and of course, there’s a PhET simulation:) https://phet.colorado.edu/en/simulation/discharge-lamps
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
• Discharge lamp result: we see well-separated spectral lines at certain colors, not a continuum of light frequencies!
• Simplest example above: hydrogen spectrum (only a single electron). Spectrum depends on which element we put in the lamp.
• What does this result imply about the behavior of the electron inside the atom?
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PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 18
Electrons in an atom must have discrete energy levels!
In terms of our “solar system” picture, this implies that only certain electron orbits are allowed.
(Remember the particle in a box? Only certain “electron wave” wavelengths allowed, maybe?)
Eu^
or. - - - - - - > r
! .
"
¥i= If f -
z- Ez
- E,
-- •
^ e/ - E
,
ground state
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
In 1913, Bohr proposed an atomic model which adds the following empirical rules to Rutherford’s atom:
1. Atomic electrons exist in stationary states, labelled by an integer n.
2. The electron in state n has energy En, with E1<E2<E3…
3. The lowest-energy state n=1 is stable.
n = “quantum number”•
•
TO •
÷:=3
.
:
•MmY• +0 +0 ;•n→• +0
it it #to
↳ •
,
• ← TO +0 +0
absorption emission collision20
E free e
-
←
mmmmo - -
÷. - -
- E,
-
- Ez -
- E,
--
fground state
:↳ ;,¥÷!d.
.f⇐⇐⇐⇐÷⇐¥a
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure 21
4. Electrons can jump between energy levels by emitting (or absorbing) a photon.
6. Excited electrons will jump quickly (but unpredictably!) to lower-energy states, until
they reach the ground state.
f =�E
h
Very quickly, usually on the order of nanoseconds.
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5. Electrons can jump up by absorbing kinetic energy from colliding with another particle.
•
•
TO •
÷:=3
.
:
•MmY• +0 +0 ;•n→• +0
it it #to
↳ •
,
• ← TO +0 +0
absorption emission collision
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
CQ: A certain type of atom has the energy levels shown below. The atom starts in the ground state.
We illuminate the atom with a light source producing 8 eV photons. How many different light colors can the atom produce
after we illuminate it?
• A. No light is produced
• B. 1 color
• C. 2 colors
• D. 3 colors
• E. 4 colors
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Fledij÷÷:
•
•
TO •
÷:=3
.
:
•MmY• +0 +0 ;•n→• +0
it it #to
↳ •
,
• ← TO +0 +0
absorption emission collision
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
CQ: A certain type of atom has the energy levels shown below. The atom starts in the ground state.
We put the atom in a discharge lamp, where an 8 eV electron collides with it. How many different light colors can the atom
produce after the collision?
• A. No light is produced
• B. 1 color
• C. 2 colors
• D. 3 colors
• E. 4 colors
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Fledij÷÷:Emax
-2 eV=
•
•
TO •
÷:=3
.
:
•MmY• +0 +0 ;•n→• +0
it it #to
↳ •
,
• ← TO +0 +0
absorption emission collision
PHYS 2130 - Fall 2017Lecture 10: Atomic Structure
CQ: A certain type of atom has the energy levels shown below. The atom starts in the ground state.
We illuminate the atom with white light, and measure the colors of light which are not absorbed. How many different light colors
are missing from the spectrum we measure?
• A. No light is produced
• B. 1 color
• C. 2 colors
• D. 3 colors
• E. 4 colors
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Fledij÷÷:
•
•
TO •
÷:=3
.
:
•MmY• +0 +0 ;•n→• +0
it it #to
↳ •
,
• ← TO +0 +0
absorption emission collision
(note: we skipped this one in class.)