R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Session 37 Models of atoms

Dec 1, 2011

Electron tracks in a cloud chamber (1937) sciencemuseum.org.uk

Announcements

•! Exam 3 score files posted today •! Average 77, std dev 13.5

•! Final exam is NOT droppable! Everyone must take the final. •! Final will be about 1/3 on material since exam 3, remainder covers

all material discussed during the course

•! As usual there will be a review session last day of term, and

formula page(s?) will be posted

!"

Lecture Schedule (to end of term)

!"#$%&

1. When a beam of light, which is traveling in air, is reflected by a glass surface, there is"

A) a 90° phase change in the reflected beam."

B) no phase change in the reflected beam."

C) a 180° phase change in the reflected beam."

D) a 60° phase change in the reflected beam."

E) a 45° phase change in the reflected beam."

Answer: C"

Phase change ! = 180° for reflection off a higher index medium."2. A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are

small, by what factor will the width of the central bright spot on the screen change if the slit width is

doubled?"

A) It will be cut to one-quarter its original size."

B) It will be cut in half."

C) It will double."

D) It will become four times as large."

E) It will become eight times as large."

Answer: B"

!""

3. Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit

should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of

the screen?"

A) 0.39 m"

B) 0.93 m"

C) 1.1 m"

D) 1.5 m"

E) 1.9 m"

Answer: B"

4. A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the

film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and

water are 1.40 and 1.33, respectively, what is the minimum thickness of the film to see a bright reflection?"

A) 100 nm"

B) 200 nm"

C) 300 nm"

D) 400 nm"

E) 500 nm

Answer: A (see Figure 28-14 and related discussion in textbook)

5. A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for

this telescope at a wavelength of 620 nm?"

A) 1.11 " 10-7 rad"

B) 3.11 " 10-7 rad"

C) 2.70 " 10-7 rad"

D) 1.35 " 10-7 rad"

E) 4.05 " 10-7 rad"

Answer: D"

n=1.40"

6. Which one of the following statements is false?"

A) The laws of physics are the same in all inertial frames of reference."

B) Observers in different inertial frames can disagree about the location of an event."

C) Observers in different inertial frames can disagree about the time separating two events."

D) Einstein's theory of special relativity applies to accelerated frames of reference."

E) Relativistic time dilation does apply to biological processes."

Answer: D (special relativity is for inertial frames; general relativity covers accelerated frames)"

7. Observer A sees a ruler moving by in a relativistic train and measures its length to be LA. Observer B moves

together with the train and measures the length of the ruler to be LB. These two results will be such that"

A) LA > LB. "

B) LA = LB. "

C) LA < LB. "

D) LA could be greater or smaller than LB depending on the direction of the motion. "

Answer: C"

8. You are moving at a speed (2/3)c relative to Randy, and Randy shines a light toward you. At what speed do you see the

light passing you by?"

A) (1/3)c"

B) (2/3)c"

C) (4/3)c"

D) c"

E) It depends on whether you are moving towards or away from Randy."

Answer: D"

9. Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on

Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific instruments, including a meter

stick. Now that Jill is underway, how long does she measure the meter stick to be?"

A) 1.00 m"

B) 0.960 m"

C) 1.04 m"

D) 0.280 m"

E) 1.28 m"

Answer: A

Meter stick is in Jill’s frame – an Earth observer would see it contracted, but not Jill.

10. At what speed is the mass of an electron double its rest mass?"

A) 0.500c"

B) 0.650c"

C) 0.707c"

D) 0.866c"

E) 0.960c"

Answer: D"

11. Which one of the following is true for the surface temperature T of a bluish-white star, as compared to a red star?"

A) Blue star#s T is greater."

B) Blue star#s T is less."

C) Blue star#s T is the same."

Answer: A"

I hope you remember (after all our discussions of spectra) that red = long wavelength, blue=short wavelength, and shorter

wavelength =higher frequency! Temperature is proportional to f:"

12. A photon has energy of 4.20 eV. To what wavelength does this energy correspond?"

A) 321 nm"

B) 103 nm"

C) 296 nm"

D) 412 nm"

E) 420 nm"

Answer: C"

13. The work function of a certain metal is 1.90 eV. What is the longest wavelength of light that can cause photoelectron

emission from this metal?"

A) 231 nm"

B) 14.0 nm"

C) 62.4 nm"

D) 344 nm"

E) 653 nm"

Answer: E"

(see practice questions!)"

14. An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength?"

A) 409 nm"

B) 302 nm"

C) 205 nm"

D) 420 nm"

E) 502 nm"

Answer: A"

(see practice questions!)"

15. A muon is an unstable particle that has an average lifetime of 1.52 " 10-6 s. This is the time interval between its creation

in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the

muon. An "average" muon is observed by a scientist on Earth to travel 342 m in its lifetime. What is the speed of the muon

relative to Earth?"

A) 0.821c"

B) 0.681c"

C) 0.601c"

D) 0.551c"

E) 0.335c"

Answer: C"

The muon#s lifetime in the Earth frame is time-dilated by the Lorentz factor, so"

11

More details on the structure of atoms

•! With the work of Schrödinger and Heisenberg, we can complete our picture

of atomic structure

–! Quantum mechanics allows exact computations for any atom, not just hydrogen

or helium: chemistry is no longer empirical

•! Each atom’s electron arrangement is described by a set of “quantum numbers” (integers or half-integers – sound familiar?)

–! Principal quantum number (energy level) n=0,1,2,3…

–! Orbital number (value of angular momentum L due to e’s orbital motion)

–! “magnetic” quantum number ml (component of L along some axis)

•! …for example, a symmetry axis: the magnetic field direction, if B is present

•! Exclusion principle -> cannot know more than 1 component of L precisely

–! “spin” quantum number ms (“internal” angular momentum of electron)

•! Only 2 values allowed: spin = +1/2 (“spin up”) or -1/2 (“spin down”)

•! Relative to axis used for l - also in units of h-bar

l =0,1,2…n

Example: hydrogen for n=1 and n=2

•! Table in text shows all the allowed “quantum states” for the single electron in a hydrogen atom

12

“Ground state” has n=1,

l =0, (only allowed value)

Spin either up or down:

2 possible states

first “excited state” has

n=2, l =0

spin either up or down:

2 possible states

next excited state has n=2,

l =1, m l = -1, 0, or +1

spin either up or down for

each value of l

6 possible states

13

Better than the popcorn ball picture…

•! Here are electron ‘orbitals’ for a hydrogen atom (maps of charge density, or probability of finding electron)

•! Numbers give the electron’s quantum energy level (here, the 2nd and 3rd)

•! Letters give its quantized angular momentum (s=0, p=1, d=2 quanta of L) –! Letters are labels from 19th c.

studies of atomic spectra

•! Quantum theory connects line spectra with levels

–! Notice:

•! s orbitals are spherically symmetrical

•! p’s have 1 axis of symmetry

•! d’s have 2 symmetry axes… etc

http://www.chemistry.mcmaster.ca/esam

Lasers: atomic physics and QM in action

•! Laser processes

–! Three possible atom-photon interactions (Einstein, 1916):

1.! Electron absorbs a photon, pops into a higher E level

2.! Electron in higher E level randomly falls to lower state, emitting a photon

3.! Electron in higher E level falls to ground state and emits a photon when stimulated by a photon of the same wavelength

For spontaneous emission, the emitted photon is in phase: the photons are coherent

–! To get useful light output, we must “pump” atoms into a metastable* higher state: population inversion

–! Optical pumping: use flash lamp to raise atoms to a state E2 above E1 = metastable state

Absorption Spontaneous emission Stimulated emission

(in phase)

normal state occupancy population inversion

E1 E0

E2 E1 E0

E2

% of atoms % of atoms

*not stable like the ground

state, but comparatively

long average lifetime

15

Nucleus:

6 protons 6 neutrons

Cloud of 6 electrons

"Cloud" of one

electron

(probability of finding it at some

point near nucleus)

Nucleus =

1 proton

10-10 m

Review: Elements are identified by number of protons in the atom’s nucleus: Atomic Number = Z

•! Hydrogen: Z=1

–! 1 proton & 1 electron

–! Simplest nucleus

•! Atomic "weight" A = (#n + #p)

–! hydrogen has A=1 also (no neutrons)

•! Carbon has 6 protons

–! Z=6, most commonly A=12

•! this is 12C ("carbon-12")

•! rarer isotopes exist

–! same Z, more or fewer n's

–! e.g., 14C has 8 n's

Not to scale! 10-15 m

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atom

...but atoms themselves have constituents

•! We can use electric forces to separate an electron from an atom for study...

•! As far as we know, electrons are indeed fundamental

–! No substructure or constituents

–! Act like point particles when free from atoms

–! Easy to remove and accelerate: we can use them as projectiles

nucleus

Cloud of orbital electrons nucleus

ion (atom with less than a full set of e's)

free electron

(ionization)

atom

fewer electrons

+

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The periodic table

•! QM description of atomic structure explains regularities observed much earlier by chemists

Dimitri Mendeleyev's original table (1869)

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Periodic Table today: organizes elements by properties and atomic weight

Z and A increase as you go across and down.

Elements in same column have similar properties. http://www.molres.org/MRI_DownloadPT.html

Z

A

“Rare earth”

elements go

in here

(Parenthesis means unstable element)

Uranium is heaviest

natural element

(white numbers = synthetic elements)

“Noble

gases”:

refuse to mix with

other

elements!

(they have

electrons filliing all

allowed

states)

(# of protons)

(total n+p)