Overview

Nucleus = Protons+ Neutrons

nucleons

A = nucleon number (atomic mass number)

Gives you mass density of element

Z = proton number (atomic number) Gives chemical properties (and name)

N = neutron number

A=N+Z

Recall: Nuclear Physics

Li63

A

Z

Periodic_Table

A material is known to be an isotope of lead

Based on this information which of the following can you specify?

1) The atomic mass number

2) The neutron number

3) The number of protons

Hydrogen atom: Binding energy =13.6eV

Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!

2.2106eV

Simplest Nucleus: Deuteron=neutron+proton(Isotope of H)

neutron proton

Very strong force

Coulomb force

electronproton

Strong Nuclear Force

(of electron to nucleus)

Can get 4 nucleons into n=1 state. Energy will favor N=Z

Pauli Principle - neutrons and protons have spin like electron, and thus ms= 1/2.

n n p p

n n p p

But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z.

# protons = # neutrons

7

ground state

2.2 MeV

Deuteron Binding Energy

Nuclei have energy level (just like atoms)

12C energy levels

Note the energy scale is MeV rather than eV

energy needed to remove a proton from 12C is 16.0 MeV

energy needed to remove a neutron from 12C is 18.7 MeV

Where does the energy released in the nuclear reactions of the sun come from?

(1)covalent bonds between atoms

(2)binding energy of electrons to the nucleus

(3)binding energy of nucleons

Binding Energy

Einstein’s famous equation E = m c2

Proton: mc2 = 938.3MeVNeutron: mc2= 939.5MeV

Deuteron: mc2 =1875.6MeV

Adding these, get 1877.8MeV

Difference is Binding energy, 2.2MeV

MDeuteron = MProton + MNeutron – |Binding Energy|

proton:mc2=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J

ACT: Binding Energy

Which system “weighs” more?

1) Two balls attached by a relaxed spring.

2) Two balls attached by a stretched spring.

3) They have the same weight.

Iron (Fe) has most binding energy/nucleon. Lighter have too few nucleons, heavier have too many.

BIN

DIN

G E

NE

RG

Y in

MeV

/nu

cleon

92238U

10

Binding Energy Plot

Fission

Fusi

on Fusion = Combining small atoms into large

Fission = Breaking large atoms into small

• Neon (Z=10)

• Iron (Z=26)

• Iodine (Z=53)

Which element has the highest binding energy/nucleon?

Which of the following is most correct for the total binding energy of an Iron atom (Z=26)?

9 MeV

234 MeV

270 MeV

504 Mev

particles: nuclei 24He

particles: electrons

: photons (more energetic than x-rays) penetrate!

3 Types of Radioactivity

Easily Stopped

Stopped by metal

Radioactive sources

B field into screen

detector

92238U 90

234Th: example

24He recall

: example

Decay Rules

1) Nucleon Number (A) is conserved.2) Atomic Number (Z) is conserved.3) Energy and momentum are conserved.

: example 00

* PP AZ

AZ

1) 238 = 234 + 4 Nucleon number conserved

2) 92 = 90 + 2 Charge conserved

e0111

10 pn

Needed to conserve momentum.

00

A nucleus undergoes decay. Which of the following is FALSE?

1. Nucleon number decreases by 4

2. Neutron number decreases by 2

3. Charge on nucleus increases by 2

The nucleus undergoes decay. 90234Th

Which of the following is true?

1. The number of protons in the daughter nucleus increases by one.

2. The number of neutrons in the daughter nucleus increases by one.

ACT: Decay

Which of the following decays is NOT allowed?

HePbPo 42

21082

21484

92238U 90

234Th

40 40 0 019 20 1 0K P e

NC 147

146

1

2

3

4

Nt

N

If the number of radioactive nuclei present is cut in half, how does the activity change?

1) It remains the same

2) It is cut in half

3) It doubles

No. of nuclei present

decay constant

Decays per second, or “activity”

Radioactive decay rates

Preflight 27.8

ACT: Radioactivity

Start with 16 14C atoms.

After 6000 years, there are only 8 left.

How many will be left after another 6000 years?

1) 0 2) 4 3) 8

Nt

N

No. of nuclei present

decay constant

Decays per second, or “activity”

time

N(t)N0e t N0 2

t

T1/2

Decay Function

Instead of base e we can use base 2:

N(t)N0e tSurvival:

No. of nuclei present at time t

No. we started with at t=0

e t 2

tT1/2

T1/2

0.693

where

Then we can write N(t)N0e t N0 2

t

T1/2

Half life

Radioactivity Quantitatively

Nt

N

No. of nuclei present

decay constant

Decays per second, or “activity”

The half-life for beta-decay of 14C is ~6,000 years. You test a fossil and find that only 25% of its 14C is un-decayed. How old is the fossil?

1. 3,000 years

2. 6,000 years

3. 12,000 years

Summary• Nuclear Reactions

– Nucleon number conserved– Charge conserved– Energy/Momentum conserved– particles = nuclei– - particles = electrons– particles = high-energy photons

• Decays– Half-Life is time for ½ of atoms to decay

N(t)N0e tSurvival:

T1/2

0.693

24He