Physics 102: Lecture 27, Slide 1

Nuclear Binding, Radioactivity

Physics 102: Lecture 28

Physics 102: Lecture 27, Slide 2

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

AZ

Periodic_Table

Physics 102: Lecture 27, Slide 3

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 number2) The neutron number3) The number of protons

Preflight 27.1

Physics 102: Lecture 27, Slide 4

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)

Physics 102: Lecture 27, Slide 5

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

Physics 102: Lecture 27, Slide 6

ground state2.2 MeV

Deuteron Binding Energy

Physics 102: Lecture 27, Slide 7

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

Physics 102: Lecture 27, Slide 8

Preflight 27.2

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

Physics 102: Lecture 27, Slide 9

Binding EnergyEinstein’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

Physics 102: Lecture 27, Slide 10

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.

Physics 102: Lecture 27, Slide 11

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

BIND

ING

ENER

GY in

MeV

/nuc

leon

92238U

10

Binding Energy Plot

Fission

Fusio

n

Fusion = Combining small atoms into largeFission = Breaking large atoms into small

Physics 102: Lecture 27, Slide 12

• Neon (Z=10) • Iron (Z=26)• Iodine (Z=53)

Which element has the highest binding energy/nucleon?

Preflight 27.3

Physics 102: Lecture 27, Slide 13

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

9 MeV234 MeV270 MeV504 Mev

Preflight 27.4

Physics 102: Lecture 27, Slide 14

particles: nuclei 24He particles: electrons : photons (more energetic than x-rays) penetrate!

3 Types of Radioactivity

Easily StoppedStopped by metal

Radioactive sources

B field into screen

detector

Physics 102: Lecture 27, Slide 15

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

Physics 102: Lecture 27, Slide 16

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

Preflight 27.6

Physics 102: Lecture 27, Slide 17

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.

Preflight 27.7

Physics 102: Lecture 27, Slide 18

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

Physics 102: Lecture 27, Slide 19

Nt N

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

1) It remains the same2) It is cut in half3) It doubles

No. of nuclei present

decay constant

Decays per second, or “activity”

Radioactive decay rates

Preflight 27.8

Physics 102: Lecture 27, Slide 20

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”

Physics 102: Lecture 27, Slide 21 time

N(t)N0e t N0 2

tT1/2

Decay Function

Physics 102: Lecture 27, Slide 22

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

tT1/2

Half life

Radioactivity Quantitatively

Nt N

No. of nuclei present

decay constant

Decays per second, or “activity”

Physics 102: Lecture 27, Slide 25

ACT/Preflight 27.9

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 years2. 6,000 years3. 12,000 years

Physics 102: Lecture 27, Slide 26

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