Lecture 3: E=mc2 & The atomic bomb

Today’s song:Einstein Brain - Admiral Freebee

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Practicalities

• Thursday reading: Chapter 4 of lecture notes

• Bring a laptop if you have one, and install the “radioactive dating game” (Instructions on worksheet, see Sakai)

• First draft blog is due today at 5pm.

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A. There is always the same amount of protons and neutrons in a nucleus

B. The nucleus is about the same size as the atom

C. Protons and neutrons both have positive charge

D. Protons are positively charged, electrons are negatively charged and neutrons are electrically neutral

E. My favorite element is Krypton

Which of these statements is true?

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A. There is always the same amount of protons and neutrons in a nucleus

B. The nucleus is about the same size as the atom

C. Protons and neutrons both have positive charge

D. Protons are positively charged, electrons are negatively charged and neutrons are electrically neutral

E. My favorite element is Krypton

Which of these statements is true?

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A. In an atomic bomb, the energy is produced by splitting nuclei while a star draws most of its energy from gravity

B. In an atomic bomb, the energy is produced by splitting nuclei while a star draws most of its energy from fusing nuclei

C. E=mc2 is important for an atomic bomb, but not for a star

D. There is no major difference

E. Oprah is a star, but not an atomic bomb

What is the most important difference between an atomic bomb (Uranium or Plutonium) and a star, when it comes to

energy production?

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A. In an atomic bomb, the energy is produced by splitting nuclei while a star draws most of its energy from gravity

B. In an atomic bomb, the energy is produced by splitting nuclei while a star draws most of its energy from fusing nuclei

C. E=mc2 is important for an atomic bomb, but not for a star

D. There is no major difference

E. Oprah is a star, but not an atomic bomb

What is the most important difference between an atomic bomb (Uranium or Plutonium) and a star, when it comes to

energy production?

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Last time you learned...

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Review Uncertainty

Uncertainties limit our ability to predict stuff

From coarse graining:

man made uncertainties, due to imperfect experiments/computers

From quantum mechanics:

Hard wired into Nature itself

Both types of uncertainties can and must be controlled to estimate the accuracy of our predictions

Confirmed in numerous experiments!

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The plan of actionLecture 2:

Quantum Mechanics & UncertaintyLecture 3:

E=mc2 & the atomic bomb

Workshop: Radioactivity

Lecture 4: The Fukushima disaster

Lecture 5: Intro to modern Particle Physics

Lecture 1: Intro to Quantum Mechanics

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Atomic structure (lightning review)

Electrons (charge -1)

Protons (charge +1)

Neutrons (charge 0)

Electrically Neutral

Drawing not to scale!

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A. The nucleus is electrically neutral

B. The total electric charge of the nucleus is positive 8

C. The total charge of the nucleus depends on the amount of neutrons in the nucleus

D. The total charge of the nucleus depends on the amount of electrons in the atom

E. Oxygen, who needs that anyways?

The element Oxygen has atomic number 8, which means its nucleus has 8 protons. Which of these statements about Oxygen

is true?

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A. The nucleus is electrically neutral

B. The total electric charge of the nucleus is positive 8

C. The total charge of the nucleus depends on the amount of neutrons in the nucleus

D. The total charge of the nucleus depends on the amount of electrons in the atom

E. Oxygen, who needs that anyways?

The element Oxygen has atomic number 8, which means its nucleus has 8 protons. Which of these statements about Oxygen

is true?

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Isotopes

235UExample: Mass number = 235Atomic number = 92

Mass number = # protons + # neutronsAtomic number = # protons

Definition:

How many neutrons are there in a 235U nucleus?

A. 92

B. 235

C. 143

D. 327

E. There is not enough information

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Isotopes

235UExample: Mass number = 235Atomic number = 92

Mass number = # protons + # neutronsAtomic number = # protons

Definition:

How many neutrons are there in a 235U nucleus?

A. 92

B. 235

C. 143

D. 327

E. There is not enough information

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Forms of energy

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A famous equation, but what does it mean?

E = m c2

Energy! mass (speed of light)2

9x 1016 m2/s2= X

Mass is another form of energy!

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A. E = 0.5 kg x (3 x 108 m/s) x (2.8 x 10-7 kWh / J)

B. E = 0.5 kg / (3 x 108 m/s) x (2.8 x 10-7 kWh / J)

C. E = 0.5 kg x (3 x 108 m/s) / (2.8 x 10-7 kWh / J)

D. E = 0.5 kg x (3 x 108 m/s)2 x (2.8 x 10-7 kWh / J)

E. E = 0.5 kg x (3 x 108 m/s)2 / (2.8 x 10-7 kWh / J)

How much total energy (in kiloWatt hours) is there in your lunch, estimating its mass to be 0.5 kg?

E = mc2

c = 3 x 108 m/s

1 kg m2/s2 =1J = 2.8 x 10-7 kWh

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A. E = 0.5 kg x (3 x 108 m/s) x (2.8 x 10-7 kWh / J)

B. E = 0.5 kg / (3 x 108 m/s) x (2.8 x 10-7 kWh / J)

C. E = 0.5 kg x (3 x 108 m/s) / (2.8 x 10-7 kWh / J)

D. E = 0.5 kg x (3 x 108 m/s)2 x (2.8 x 10-7 kWh / J) = 1.2 x 1010 kWh

E. E = 0.5 kg x (3 x 108 m/s)2 / (2.8 x 10-7 kWh / J)

E = mc2

c = 3 x 108 m/s

1 kg m2/s2 =1J = 2.8 x 10-7 kWh

1.2 x 1010

Roughly the energy needed to power the entire country for a few hours!

How much total energy (in kiloWatt hours) is there in your lunch, estimating its mass to be 0.5 kg?

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Is there is so much energy around us, why do we still have an energy crisis?

E = m c2 tells us that mass is a form of energy...

... but it doesn’t tell us how to transform it into a useful form of energy, like kinetic

energy or electrical energy.

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Radioactivity

Marie Curie(1867-1934)

Nobel Prize 1903 and 1911

Henri Becquerel(1852-1908)

Nobel Prize 1903

α

235U

In radioactive decays, a small amount of mass gets converted into kinetic energy!

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Radioactive decays at the earths core drives geological processes

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The Barium problem

Otto Hahn(1879-1968)

Nobel Prize 1944

Lise Meitner(1878-1968)

n

n

n

235U

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Dear Lise,

... There is something about the "Radium isotopes" that is so remarkable that for now we are only telling you... Perhaps you can suggest some

fantastic explanation ... If there us anything you could propose that you could publish, than it would still in a way be work by the three of us!

Otto HahnDecember 19th,1938

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Could it split?

235U

92Kr

141Ba

Where would the energy come from?

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Can a small stone break a giant rock?

a neutron is 235 times less massive than 235U!

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A nucleus has properties similar to a drop of liquid

Another example of a model!

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The liquid drop model

But still the energy budget does not add up ...

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E = mc2 makes up for the energy deficit!

Christmas time 1938Kungälv, Sweden

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Yes it can split!

235U

92Kr

141Ba

The sum of the masses of the daughters is slightly less that the mass of the mother nucleus

Mass got converted into energy!

Nuclear fission

extra neutrons

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A chain reaction

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A. 2 x 3 = 6

B. 3 x 3 = 9

C. 2 x 2 x 2 = 8

D. 3 x 3 x 3 =27

E. The only split I care about is the one involving bananas and ice cream

When a Uranium nucleus splits, it produces 3 neutrons. Assuming that only 2 out of 3

neutrons hit another Uranium nucleus, how many nuclei will have split after 3

“generations” of splittings?

Hint: Making a drawing helps here!

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A. 2 x 3 = 6

B. 3 x 3 = 9

C. 2 x 2 x 2 = 8

D. 3 x 3 x 3 =27

E. The only split I care about is the one involving bananas and ice cream

When a Uranium nucleus splits, it produces 3 neutrons. Assuming that only 2 out of 3

neutrons hit another Uranium nucleus, how many nuclei will have split after 3

“generations” of splittings?

After 20 generations, one splitting will have resulted in over a million new splittings.

Hint: Making a drawing helps here!

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F.D. Roosevelt President of the United States White House Washington, D.C. August 2th, 1939

Sir:

Some recent work ... which has been communicated to me in manuscript, leads me to expect that the element Uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation which has arisen seem to call for watchfulness and, if necessary, quick action on the part of the administration... This new phenomenon would ... lead to the construction of bombs ... A single bomb of this type, carried by boat and exploded in a port, might well destroy the whole port together with some of its surrounding territory....

Yours very truly Albert Einstein

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The White House Washington October 19th, 1939

My dear Professor,

I want to thank you for your recent letter and the most interesting and important enclosure. I found this data of such import that I have convened a board...

... Please accept my sincere thanks.

Very sincerely yours, Franklin Roosevelt

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Germany

Werner Heisenberg(1901-1976)

Nobel Prize 1932

Neutrons usually miss the nucleus, and the chain reaction does not occur

Major Problem:

Atoms are mostly made of empty space!

Solution:

• stack 235U nuclei as close together as possible

• slow down the neutrons

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Germany

Werner Heisenberg(1901-1976)

Nobel Prize 1932

Neutrons usually miss the nucleus, and the chain reaction does not occur

Major Problem:

Atoms are mostly made of empty space!

Solution:

• stack 235U nuclei as close together as possible

• slow down the neutrons

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Critical mass:

The smallest amount of 235U needed to sustain the chain reaction

If (on average) less than one neutron per splitting hits another Uranium nucleus, what will happen with

the chain reaction?

A. The amount of nuclei that split each second will fall to zero quickly

B. The amount of nuclei that split each second will remain constant

C. The amount of nuclei that split each second will increase rapidly

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Critical mass:

The smallest amount of 235U needed to sustain the chain reaction

If (on average) less than one neutron per splitting hits another Uranium nucleus, what will happen with

the chain reaction?

A. The amount of nuclei that split each second will fall to zero quickly

B. The amount of nuclei that split each second will remain constant

C. The amount of nuclei that split each second will increase rapidly

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Fast neutrons just race by the Uranium nuclei

They must be slowed down!

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Put the neutrons in the NYC subway during rush hour

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... or equivalently:

Make them bump into something else

Vemork, Norway

heavy water

(as much as possible)

regular water heavy water

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Vemork, Norway

Knut Haukelid(1911-1994)Heavy water supply destroyed by Norwegian

resistance on February 28th 1943

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America: The Manhattan Project

Robert Oppenheimer(1904-1967)

First example of “Big Science”• Large budget, hundreds of scientists• International

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An alternative to 235U

235U• occurs in nature• hard to purify• once purified, easy to

detonate

239Pu• man made element• very unstable• hard to detonate

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Lake Tinn

Norwegian resistance sank the ferry with Germany’s heavy water supply on lake Tinn

on February 21th 1944

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“Trinity” testNew Mexico, 05:30 on 16 July 1945

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“little boy” August 6th 1945

Hiroshima

between 90 000 and 166 000 casualties

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“Fat Man” August 9th 1945

Nagasaki

between 60 000 and 80 000 casualties

Japan surrendered on August 15th 1945

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Our sun

http://www.youtube.com/watch?feature=player_embedded&v=tY2n2CHMXfI

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What is it made off?

Where does it get all its energy from?

(You will learn how to figure this out yourself in module 3!)

27% Helium

72% Hydrogen

2% Other elements

As a whole

50% Helium

50% Hydrogen

In the core

The sun turns Hydrogen into

Helium

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Nuclear fusion

2H + 3

H → 4He+ n

The sun is steadily turning its Hydrogen into Helium!

and it uses E=mc2 to convert mass into energy!52

Even the stars come to an end...

at some point, even the sun experiences an energy crisis....

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So the sun is a Helium factory...

.. but where does all the other stuff come from?

Betelgeuse

Orion Constellation

Red Giants

Very massive stars

Burn Hydrogen much faster

Much shorter lifetimes!

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The ultimate doom of a giant

IronIron is the most stable element

Fusing Iron into a heaver element costs energy!

After millions of years, the star has eventually ran out of all her sources of energy

Its own gravitational attraction seals its fate... 55

Supernovas

Converts energy into mass!

Create all heavy

elements

July 4th 1054

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http://www.youtube.com/watch?v=9D05ej8u-gU&feature=player_embedded

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See you on Thursday for the workshop on Radioactivity

Bring a laptop if you have one

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