Special Event!

“The Universe is a Strange Place”

Frank Wilczek

Feshbach Professor of Physics, MIT

Winner of the 2004 Nobel Prize in Physics

Today, 3:00pm

LeMay Auditorium

So what is an atom?

• Typical size: 10–10 m– Alternate name: 1 Angstrom (Å)

• But what are they?

• Maybe small, solid, indivisible lumps?– What gives them different chemical properties? Shapes, maybe?

• Or, do atoms have pieces that can be taken apart?– If so, what are the pieces?

– How are they put together?

– Are the pieces made of even smaller pieces??

Electric Charges

• Electrolysis – the separation of compounds into constituent atoms using an electric current – showed that atoms could become electrically charged– Objects that are charged exert forces on each other

• Like charges repel, opposites attract

– Basic phenomena known since ancient times• For example, rub a piece of amber in fur static electricity

– There seemed to be a basic “unit” of charge, i.e. a standard chunk of charge e, so that any amount of charge is just some multiple of e

• So 1e, 2e , 3e, … but never 1.25e, for example

Cathode Rays• Phenomenon of “cathode rays” known since around 1865

• A sort of beam (“ray”) produced by an electrical discharge in a tube of gas at low pressure

• Basically like the picture tube on your TV

• But what are they?!

J.J. Thomson

Thomson’s cathode ray tube

The Electron

• J. J. Thomson showed (1897) that cathode rays were particles with electric charge – “electrons”

• Argued that electrons came from the gas atoms

• Measured the ratio of their charge to their mass

"...we have in the cathode rays matter in a new state, a state in which the subdivision of matter is carried very much farther than in the ordinary gaseous state: a state in which all matter – that is, matter derived from different sources such as hydrogen, oxygen, etc. – is of one and the same kind; this matter being the substance from which the chemical elements are built up."

– J.J. Thomson (1897), "Cathode Rays," Philosophical Magazine 44, 295

The Electron

• Later, Robert Millikan measured the charge of the electron directly– A student at Oberlin College

– Later professor at U. of Chicago, then Caltech

• Led to the determination of the mass of the electron

• About 1/2000 the mass of hydrogen (!)

• Showed that all charges, positive and negative, come in multiples of the basic e

Millikan’s Paper

Models of the Atom

• So atoms do have pieces – electrons, at least

• These pieces don’t account for much of the mass of an atom, though!

• Atoms are electrically neutral; since electrons are negative, there must be something positive as well

• Thomson proposed a “plum pudding” model– Electrons are embedded like plums in a

pudding, or blueberries in a muffin

• But how to test it??

Scattering

• Basic idea: bombard atoms with projectiles

• Depending on what’s inside, the projectiles will be deflected in various ways

• Reconstruct the internal structure of the atom from the pattern of scattered objects

• Still the way we study small systems today!

ErnestRutherford

• Born to a poor family in New Zealand

• A student of J. J. Thomson at Cambridge

• Spent time at McGill University in Canada and the University of Manchester

• Later returned to Cambridge as head of the Cavendish Lab

• Nobel Prize in chemistry (1908)

• Supervised an unusually large number of future Nobel winners

• Known for his somewhat caustic wit

"All science is either physics or stamp collecting."

Rutherford’s Experiment (1910)• With Hans Geiger and Ernest Marsden

• Shot “ particles” at a thin gold foil particle = nucleus of helium

– 8000 times as heavy as an electron

– About 50 times lighter than a gold atom

– Positive charge

• Looked at pattern of scattered ’s

What did he expect to find?• If Thomson’s picture is correct, we expect very little scattering

– Since particles are much heavier than electrons, the electrons just get brushed aside – we can ignore them!

– Positive charge “the muffin” is very spread out, diffuse

– The incoming particle should just blow right through it

– Very little net deflection, on average• Theory suggests a few degrees at most

Incoming particleOutgoing particle

1-2 degrees

What did he find?• Most (99.99%) particles are deflected only slightly

• Some, however, are deflected through very large angles!

"It was quite the most incredible event that ever happened to me in my life. 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."

Incoming particle

Outgoing particle

What does it mean?

1. Most of the atom is empty space– Because most of the particles were not deflected significantly

2. The positive charge in the atom is concentrated in a tiny nucleus– Only a high concentration of charge can produce the large

scatterings seen occasionally

3. The nucleus has a large mass, almost the entire mass of the atom in fact– Otherwise the particle would brush it out of the way

A very unexpected result, basically the opposite of Thomson’s model!

Animation

A New Model

• Rutherford’s analysis showed that the size of the nucleus is about 100,000 times smaller than the atom as a whole– About 10–10 / 105 = 10–15 m

– If we could scale up the atom so that the nucleus was the size of a golf ball, the atom would be about five miles across!

• Atom = nucleus plus electrons– Nucleus is heavy, positively charged

– Electrons are light and negatively charged

• How is it put together??

• Analogy: the solar system

• Solar system contains planets plus the sun– Sun is much more massive

than any planet

• Force of gravity holds them in orbit– Planets are attracted to the sun

• Force falls off like the square of the distance from the planet to the sun

Planetary Orbits

2d

MGMF planetsun

Electrical Attraction

• Interestingly, the force of attraction between electric charges has almost the same form!

221

d

QkQFel

Q1

Q2

d

2d

MGMF planetsun

grav

Compare to:

Hmmm...

“Planetary Model” of the Atom

• Atom like a miniature solar system – electrons orbiting nucleus

• Electrical attraction holds it together– Opposites attract

• Same type of orbits as for planets, even

• A dynamic atom, not static

• Chemical properties perhaps connected to electron orbits?

A Problem• It won’t work!

• There are (three) additional equations describing electrical and magnetic phenomena – Maxwell’s equations– Unify electric, magnetic, and optical phenomena

– Light is an electromagnetic wave

• An electron moving in an orbit would give off light

• The light carries energy away from the electron

• The electron spirals closer to

the nucleus and eventually

crashes into it

• This would all happen in

much less than a second!

So what’s the answer?

• Rutherford and his contemporaries had no solution to this problem

• Solving it required an entirely new type of physics theory – Quantum Mechanics

• In this theory, the electrons don’t really “orbit,” rather, they are “spread out” in a sort of cloud around the nucleus

• You always find whole electrons, though!

• In a sense, the electron is nowhere (everywhere?) until we look for it

• Weird, but QM is the most precisely tested scientific theory of all time!

“Hard Cylinder” Scattering

• A (relatively!) simple model that is analogous to Rutherford’s experiment and analysis

• Consider scattering of steel balls (say) off a heavy, perfectly elastic cylinder

Ball( particle)

Cylinder(Nucleus)

Analysis

• Let’s determine the pattern of scattered particles in this case, i.e. how they deflect

• If we see this pattern, we could conclude that the nucleus is cylindrical (round)– Also that the scattering (interaction) is of “hard cylinder” type

• In this simple case, the scattering behavior can be determined from the geometry alone

• In the real-world case, the scattering pattern follows from knowing the force between the particle and nucleus– Just the electrical repulsion

– A bit more complicated…

Basic Setup

b

Scattering angleThese angles are equal!

Outgoing direction

R

So we can determine what is for any b

Result

• This geometry exercise is not terribly interesting • Result:

(For the record, I have neglected the size of the ball compared to R in this.)

• Gives b for any , or vice versa:

)2cos(Rb

)arccos(2 Rb

Check #1

• If b = 0 we should get = 180

b

= 180

Does the formula work?

• If b = 0 then

• Thus

)2cos(Rb

0)2cos(

180 Yep!

Check #2

• If b = R we should get = 0

b

b = R

= 0

Does it work?

• If b = R then

• Thus

)2cos(Rb

1)2cos(

0 Yep!

Putting it to Use

• Assume that we couldn’t see the heavy cylinder!

• Scatter balls off it for lots of different b’s

• Note the outgoing directions of the scattered particles

• If we find that b and obey the relation

then we conclude the nucleus is round and the scattering of “hard sphere” type!

)2cos(Rb

Size of the Nucleus

• The formula says that b is proportional to cos(/2)

• So if we plot b versus cos(/2) we should get a straight line with slope equal to R

)2cos(Rb

b

cos(/2)

Allows us to determine the size R of the “nucleus”!

Sample Datab (cm) th (deg) cos(th/2)3.009 32.95 0.95902.868 46.70 0.91812.727 64.40 0.84622.586 74.94 0.79372.445 85.14 0.73642.304 89.27 0.71162.163 98.09 0.65552.022 103.48 0.61931.881 112.53 0.55541.740 117.34 0.52001.599 123.99 0.46961.458 130.86 0.41581.317 138.54 0.35401.176 142.04 0.32531.035 147.25 0.28190.894 153.09 0.23260.753 156.88 0.2004

Scattering Angle versus b

0.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00

0.000 1.000 2.000 3.000 4.000

b (cm)

Th

eta

(d

eg

ree

s)

“Nuclear” Size Determinationb (cm) th (deg) cos(th/2)3.009 32.95 0.95902.868 46.70 0.91812.727 64.40 0.84622.586 74.94 0.79372.445 85.14 0.73642.304 89.27 0.71162.163 98.09 0.65552.022 103.48 0.61931.881 112.53 0.55541.740 117.34 0.52001.599 123.99 0.46961.458 130.86 0.41581.317 138.54 0.35401.176 142.04 0.32531.035 147.25 0.28190.894 153.09 0.23260.753 156.88 0.2004

Size Measurement

y = 2.9466x + 0.218

R2 = 0.9979

0.0000.5001.0001.5002.0002.5003.0003.500

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000

cos(theta/2)

b (

cm

)

Slope = 2.95 soR = 2.95 cm