lecture 10: atomic structure - colorado.edu€¦ · lecture 10: atomic structure phys 2130 - fall...

Lecture 10: Atomic Structure

PHYS 2130: Modern PhysicsProf. Ethan Neil

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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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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


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.

4

“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.


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!


(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

?

?

https://commons.wikimedia.org/wiki/File:Geiger-Marsden_experiment.svg


(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


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)


Rutherford’s “solar system” model

10

• 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!


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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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^

#


First problem: “death spiral”

13

• 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 (!)


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.

14

¢allowed orbits ?

,

- -

,

'

"+0-1.41 rmin? '

\/

--

-


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.

15

120Voltsvoltagedifferenceormorewithlongtube

Moving electrons Colliding with atoms

Cathode(hotwire)

Anode(plate)

(sta>onary)Atoms


(and of course, there’s a PhET simulation:) https://phet.colorado.edu/en/simulation/discharge-lamps

https://phet.colorado.edu/en/simulation/discharge-lamps


• 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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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


Bohr’s atomic model

19


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


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.

21

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


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

22

Fledij÷÷:

•

•

TO •

÷:=3

.

:

•MmY• +0 +0 ;•n→• +0

it it #to

↳ •

,

• ← TO +0 +0




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?


• B. 1 color

• C. 2 colors

• D. 3 colors

• E. 4 colors

23

Fledij÷÷:Emax

-2 eV=

•

•

TO •

÷:=3

.

:

•MmY• +0 +0 ;•n→• +0

it it #to

↳ •

,

• ← TO +0 +0




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?


• B. 1 color

• C. 2 colors

• D. 3 colors

• E. 4 colors

24

Fledij÷÷:

•

•

TO •

÷:=3

.

:

•MmY• +0 +0 ;•n→• +0

it it #to

↳ •

,

• ← TO +0 +0


(note: we skipped this one in class.)


Important distinction: emission for any n —> n’ but absorption for only 1 —> n

(excited atoms go very rapidly to the ground state)

(sodium)

lecture 10: atomic structure - colorado.edu€¦ · lecture 10: atomic structure phys 2130 - fall...

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