Today: More about half-life, why atoms are radioactive, fission

Diagram of neutron-induced U-235 fission

Half-life is the average amount of time for ½ of the atoms to decay

100% remaining

50% remaining

25% remaining

12.5% remaining

Time

Isotope with long half-life

Isotope with short half-life

“Exponential Decay”

Radium-226 Where does it come from?

Half life of Radium-226 approximately 1600 years

A 30 milligram sample has a radioactivity of ~ 1 billion Bq = 109 Bq = 109 decays per second

48,000 years is about 30 half lives. Activity would decrease by a factor of 230 = about 1 billion. So, activity 48,000 years from now would be 1 Bq.

4.8 billion years ago is about 3 million half-lives. So there is no way the Radium-226 we have today existed when Earth was formed

Radium-226 Where does it come from?

So we know Radium-226 comes from somewhere else…where?

It turns out it comes from the radioactive decay of uranium in natural deposits.

Where does the Uranium come from???

http://www.youtube.com/watch?v=6SxzfZ8bRO4&feature=related

Why are some atoms radioactive?

First: Some brainstormingForm small groups, with a spokesperson

How many different forces in nature can you think of?

Can you classify them into similar groups?

Brainstorming results

-> Gravity,

Electrical, magnetic

Force that keeps protons close together in the nucleus

(All the electrical force) Intermolecular Interactions: Wind , friction, firehose, dams, earthquake forces, forces during volcanic eruptions,

Evaporation (opposing gravity somehow)

(momentum, not a force)

Metaphysical forces

First, we need to wonder why a nucleus can exist at all!

The postive charges (protons) in the nucleus are very close together! There is a LOT of electrical repulsion between two neighboring protons.

So there MUST be something else holding them together!

What holds the quarks together inside protons and neutrons?

Force Charge1 * Charge2

distance2

Same charges repel each other

http://www.youtube.com/watch?v=NiwBwSAeDu0

The strong force holds quarks together

The strong force also accounts for the nuclear forceattracts two nucleons only when they are very close(like velcro only attracts when very close together)

The strong force is one of four fundamental forces.

Strong forceElectrical forceGravitationalWeak force

(this accounts for beta decay)

Only gravity and electrical force act at long distances

Inverse-square law for gravity and electrical force.

Strong and weak die off exponentially and are only very short range (so only manifest in nuclear reactions)

Strong force is the strongest and can dominate at short range.

Gravity is the weakest force and is negligible in nuclear physics.

Clicker question—fundamental forces

Which of the following is not one of the four fundamental forces known in physics?

A) GravityB) MinorC) StrongD) ElectricalE) Weak

Why are some atoms radioactive?

Recall how excited atoms can release photons as electron goes from high potential energy to low potential energy.(Fluorescence, phosphorescence, …)

The process of emitting a photon was random for regular fluorescence / phosphorescence. In fact, it also shows exponential decay behavior.

Total energy is conserved…potential energy of the electron decreases, but a photon of energy = h * frequency is created and released.

chemeducator.org

Why are some atoms radioactive?

Some atoms are also temporarily “trapped” in a higher-potential energy state.

Via radioactive decay, they can release energy and move to a lower potential energy.

Consider alpha-decay of Uranium-238:

U23892 Th234

90 He42

The alpha particle is moving at 15,000 km/s,Having a LOT of kinetic energy

Alpha-decay

Why are some atoms radioactive?

Being trapped in a higher-energy state is a common theme in physics, chemistry, biology.

U23892 Th234

90 He42

The alpha particle is moving at 15,000 km/s,Having a LOT of kinetic energy

Alpha-decay

(heat up reaction)

Height of “activation barrier” determines reaction rate

Why are some atoms radioactive?

The nuclear (residual strong) force presents an activation barrier

Quantum mechanics allows some probability that analpha particle can “tunnel” through the barrier

Once through, electrostatic force dominates (imagine ripping apart velcro)

Take home message for “why radioactivity”

The real physics is complicated quantum mechanics…

The nucleus is held together by the nuclear force (stronger at short range than electrical)

Some heavy atoms can be in a lower potential energy if they radioactively decay.

How large the activation barrier is determines the half-life of the random process

Alpha decay can be though of as a very common but special form of nuclear fission.

Nuclear fission more generally:

An unstable nucleus splits into two “daughter nuclei”.

Except for alpha-decay, usually emits free energetic neutrons

As nuclei get larger, electrostatic force “wins”

Strong force large betweenclose protons.

Strong force much lower betweendistal protons

But electrostatic force still very high!

(Nucleons on the surface feelless strong attraction.)

You can imagine large nuclei like large soap bubbles…very floppy

Small

Medium

Large

If the nucleus randomly deforms, it can become favorable to split into two!

This is called “spontaneous” fission, and for most isotopes is very rare.

& free neutrons!!!

http://www.youtube.com/watch?v=jk6Hm1QoDYY

However, free neutrons can be absorbed and induce fission

Once physicists discovered the neutron products, they quickly realized a chain reaction was possible.

http://www.youtube.com/watch?v=HmbzJGf90Xc&feature=related (mousetraps)http://www.youtube.com/watch?v=tQa4LONy9XM&feature=related

Naturally occurring radium is a mixture of mostly U-238 and a small amount of U-235.

When U-238 absorbs a neutron, it beta-decays to Neptunium and then Plutonium:No quick emission of neutrons & no chain

reaction.

When U-235 absorbs a neutron, it very quickly undergoes fissionproducing on average 2.5 more neutronsChain reaction!

Because of mix of mostly U-238, natural uranium is not suitable for a chain reaction.

Two ways to go:

1) Separate the U-235 to make high-purity fissile material

2) Do something to make the neutrons more likely to be absorbed by U-235

For U-238 and U-235, probability of absorbing neutron depends on neutron energy

Analogous to photon absorption.

Fast neutrons (shorter wavelength): Absorbed better by U-238

Slow neutrons (longer wavelength): Absorbed better by U-235

Clicker question – Nuclear Reactor Physics

U-235 is more likely than U-238 to absorb a slow neutron.U-238 is more likely to absorb a fast neutron.Based upon the natural abundance of U-235 and U-238,

what would need to be done in a nuclear reactor to increase chance of a chain reaction?

A) Try to make all neutrons very fastB) Try to slow down neutrons

Clicker question – Nuclear Reactor Physics

U-235 is more likely than U-238 to absorb a slow neutron.U-238 is more likely to absorb a fast neutron.Based upon the natural abundance of U-235 and U-238,

what would need to be done in a nuclear reactor to increase chance of a chain reaction?

A) Try to make all neutrons very fastB) Try to slow down neutrons

This was the key to creating the first man-made controllednuclear chain reaction…neutrons were slowed down by graphite

Clicker question—Ratio of U-238 to U-235

Half-life of U-238 is about 4.5 billion yearsUranium-235 is about 700 million years.Currently natural deposits are about 0.7% U-235.Was the proportion of U-235 more or less 1

billion years ago?

A) MoreB) Less

Clicker question—Ratio of U-238 to U-235

Half-life of U-238 is about 4.5 billion yearsUranium-235 is about 700 million years.Currently natural deposits are about 0.7% U-235.Was the proportion of U-235 more or less 2

billion years ago?

A) MoreB) Less

Proportion was high enoughTo help with random creation ofNuclear reactors! (About 3% U-235)