Chapter 29: Nuclear Physics

1

•The Nucleus

•Binding Energy

•Radioactivity

•Half-life

•Biological Effects of Radiation

•Induced Nuclear Reactions

•Fission and Fusion

§29.1 Nuclear Structure

2

The atomic nucleus is composed of neutrons and protons. These particles are called nucleons.

The atom’s atomic number (Z) gives the number of protons in its nucleus. It is the atomic number that determines an atom’s identity.

3

The nucleon number or mass number is A = Z+N, where N is the number of neutrons.

Masses of atoms are sometimes give in terms of atomic mass units. 1u = 1.66053910-27 kg.

4

The mass quoted for an atom in the periodic table is a weighted average over all of the natural isotopes of that element. The weight factors are determined by using the relative abundance on Earth of each isotope.

Atoms of the same element with differing numbers of neutrons are known as isotopes.

5

For an atomic nucleus .AV

Am

This implies the density of an atomic nucleus is independent of A.

31

3

3

4

Ar

ArV

As an equality 31

0Arr

where r0=1.210-15 m = 1.2 fm

6

Example (text problem 29.2): Calculate the mass density of nuclear matter.

m 102.1 150

31 Arr

Consider a nucleus with one nucleon (A = 1).

The density is

.kg/m 103.2

m 102.134

kg 1066.1

34

317

315

27

3

r

m

7

Example (text problem 29.9): Find the radius and

volume of the nucleus.

m. 1070.5107m 102.1 151/3151/30

Arr

.m 107.73

4 3433 rV

The radius is

The volume is

Tc10743

§29.2 Binding Energy

8

A nucleus is held together by the strong nuclear force. This force only acts over distances of a few fermis.

9

The binding energy (EB) of a nucleus is the energy that must be supplied to separate it into individual protons and neutrons.

EB = Total energy of Z protons and N neutrons – total energy of nucleus.

10

Total energy of Z protons and N neutrons = (mass of Z protons and N neutrons)c2.

Total energy of nucleus= (mass of nucleus)c2.

These can be used to define the mass defect m = (mass of Z protons and N neutrons) - (mass of nucleus) so that

.2mcEB

11

12

Nucleons also obey the Pauli Exclusion Principle such that only two protons (neutrons) can occupy each proton (neutron) energy level.

Like an atom, a nucleus can be put into an excited state if it absorbs a photon of the correct energy. The nucleus can then emit a photon to go to a lower energy state.

13

14

Example (text problem 29.14): (a) Find the binding energy of the 16O nucleus.

u1370046.0

u9949146.15u0086649.1 1.00782508

atom Oneutral of mass

neutrons 8 of mass atoms H 8 of massm16

MeV 8.1272 mcEB

15

(b) What is the average binding energy per nucleon?

Example continued:

n.MeV/nucleo 986.7

nucleons ofnumber nucleonper energy Binding

BE

§29.3 Radioactivity

16

Some nuclei are unstable and decay. These nuclei are radioactive. A nucleus can emit an alpha ray, beta ray, or a gamma ray during its decay.

17

During nuclear reactions:

1. Charge is conserved.

2. The total number of nucleons is constant.

3. Energy is conserved.

Define: disintegration energy = binding energy of radioactive nucleus – total binding energy of products. This is the rest mass energy that can be converted into other forms of energy.

18

19

Alpha rays have been identified as helium nuclei.

The reaction for alpha decay is

42

42

DP AZ

AZ

Parent nucleus

Daughter nucleus

Alpha particle

20

Example (text problem 29.28): Show that the spontaneous alpha decay of 19O is not possible.

.CO 42

156

198 The reaction is

The mass of the products (including electrons) is 19.01320250u.

The mass of 19O is 19.0035787u.

The mass of the products is larger than the reactant, so this reaction cannot occur spontaneously.

21

Beta rays have been identified as either electrons (-) or positrons (+).

The reaction for beta-minus decay is

.e 00

011 DP A

ZAZ

The reaction for beta-plus decay is

.e 00

011 DP A

ZAZ

22

The neutrino and antineutrino have no charge and are nearly massless. They do not readily interact with matter.

23

During beta-minus decays, a neutron is converted into a proton.

00

01

11

10 epn

During beta-plus decays, a proton is converted into a neutron.

00

01

10

11 enp

24

Example (text problem 29.29): Calculate the maximum kinetic energy of the beta particle when decays via - decay.

.eCaK 00

01

4020

4019 The reaction is

The maximum kinetic energy of the electron is given by the disintegration energy.

K4019

25

u. 00140750.0

1920

KCa

eKeCa

MM

mMmmMm e

Example continued:

The difference between the mass of the products and the reactant is

The disintegration energy and the maximum KE of the electron is

MeV. 31.12 cmEB

26

During inverse beta decay (electron capture) a proton in a nucleus captures an electron. The reaction is

.npe 00

10

11

01

27

Gamma rays were determined to be high energy photons.

A gamma ray will be emitted when a nucleus is an excited state when making a transition to a lower energy level. For example,

.TlTl 20881

*20881

When a nucleus has experienced alpha or beta decay, it is not always left in the ground state.

§29.4 Radioactive Decay Rates and Half-Lives

28

The half-life of a sample of unstable nuclei is the time it takes for one-half of the sample to decay. The decay process is quantum mechanical and is based on probability.

29

Each radioactive nucleus has a probability per second that it will decay, called the decay constant.

unit time

decay ofy probabilitconstant decay

The number of nuclei that decay in a short time interval is

.tNN

There are statistical fluctuations in the number of decays that occur. These fluctuations are of order .N

30

The decay rate or activity is the number of radioactive decays that occur in a sample per unit time.

Nt

NR

unit time

decays ofnumber

The unit of activity is the bequerel. 1 Bq = 1 decay/sec. Another common unit is the curie. 1 Ci = 3.71010 Bq.

31

The number of nuclei remaining in a sample having N0 nuclei at t=0 is

./0

teNtN

is the mean lifetime of a nucleus.

1

Note: the above expression for N(t) is a way to determine the number of remaining nuclei only. It does not tell us which nuclei have decayed.

32

The activity at time t is /0

teRtR

where R0 is the activity at t=0.

33

It is common to write the expressions for N(t) and R(t) in terms of half-life (T1/2).

2ln2/1 T 2/12/1

2

12 00

Tt

Tt

NNtN

34

Example (text problem 29.37): Some bones discovered in a crypt in Guatemala are carbon dated. The 14C activity is measured to be 0.242 Bq per gram of carbon. Approximately how old are the bones?

/0

teRtR

Solve for t:

years270

m0.25bq/gra

bq/gram 242.0ln

2ln

years 5730ln

2ln

ln

0

1/2

0

R

tRT

R

tRt

§29.5 Biological Effects of Radiation

35

The absorbed dose of ionizing radiation is the amount of radiation energy absorbed per unit mass of tissue. Ionizing radiation is radiation with enough energy to ionize an atom or molecule.

The SI unit of absorbed dose is the Gray. 1 Gy = 1 J/kg. Another common unit is the rad (radiation absorbed dose). 1 rad = 0.01 Gy.

36

Different radiation causes different amounts of biological damage. The biologically equivalent dose measures the amount of damage caused by radiation exposure.

Equivalent dose (in sieverts) = absorbed dose (in grays)* QF.

Equivalent dose (in rem) = absorbed dose (in rads)* QF.

QF is a quality factor that is a relative measure of biological damage (200 keV x-rays have QF = 1).

37

The sievert is the SI unit of biologically equivalent dose. 1 Sv = 100 rem.

38

Alpha, beta, and gamma radiation penetrates to different depths in biological materials.

•Alpha rays are stopped by a few cm of air or about 0.02 mm of aluminum.

•Beta-minus can penetrate a few cm into biological tissue.

•Gamma ray absorption is based on probability so they can penetrate to varying depths.

39

Example (text problem 29.45): An alpha particle produced in radioactive alpha decay has a kinetic energy of typically about 6 MeV. When an alpha particle passes through matter, it makes ionizing collisions with molecules, giving up some of its kinetic energy to supply the binding energy of the electron that is removed. If a typical ionization energy for a molecule in the body is around 20 eV, roughly how many molecules can the alpha particle ionize before coming to rest?

sionization 105eV 20

MeV 6

ionizationper lost energy

particle alpha ofenergy totalsionization ofnumber

5

§29.6 Induced Nuclear Reactions

40

An unstable nucleus decays in a spontaneous nuclear reaction. An induced nuclear reaction only takes place because it is caused by a collision between a nucleus and another particle.

41

For example, p.CNn 1414

The above reaction is induced by the absorption of a neutron. This process is called neutron activation.

A spontaneous nuclear reaction will always release energy. In an induced nuclear reaction, some of the kinetic energy of the reactants is converted into rest mass of the products.

42

An exoergic reaction releases energy.

An endoergic reaction is one that requires energy to make it proceed.

43

Example (text problem 29.49): A certain nuclide absorbs a neutron. It then emits an electron, and then breaks up into two alpha particles. (a) Identify the original nucleus and the two intermediate nuclei (after absorbing the neutron and after emitting the electron).

The reactions are

.

en

42

423

01321

10

X

XXXe

f

e

f

c

d

a

b

Since the number of nucleons is conserved e = 4 + 4 = 8. Charge is conserved so f = 2 + 2 = 4. Identify X3 as Be.

44

Example continued:

In the second step of the first reaction c= e+0 = 8 and d = f - 1. This gives d = 3. Identify X2 as Li.

In the first step of the reaction a + 1 = c so a = 7 and b + 0 = d = 3. Identify X1 as Li.

The nuclei involved are

Be. Li; Li; 843

832

731 XXX

45

(b) Would any (anti)neutrino(s) be emitted? Explain.

Example continued:

In the second reaction (the beta decay of 8Li) will also involve the emission of one antineutrino.

§29.7 Fission

46

Fission is when a large nucleus splits into two smaller, more tightly bound nuclei. This process releases energy.

Fission can either occur spontaneously when the nucleus is very large, or it can be induced. When fission occurs by the capture of slow moving neutrons, a chain reaction can occur.

§29.8 Fusion

47

The process of fusion takes two small nuclei to form a larger nucleus.

48

The process of fusion is the energy production mechanism in cores of stars. Stars on the main sequence (like the Sun) turn hydrogen into helium in their cores. This occurs by the proton-proton cycle and by the CNO (carbon) cycle.

Overall, this process take four protons and turn them into a helium nucleus and energy.

49

Example (text problem 29.57): Consider the fusion reaction between a proton and a deuteron (shown below). (a) Identify the reaction product X.

XHH 21

11

The product must have 3 nucleons and a charge (atomic number) of 2. The element is He.

He32

50

Example continued:

(b) The binding energy of the deuteron is about 1.1 MeV per nucleon and the binding energy of “X” is about 2.6 MeV per nucleon. Approximately how much energy (in MeV) is released in this fusion reaction?

The binding energies are: 0 MeV for 1H; 2.2 MeV for 2H; and 7.8 MeV for 3He.

Energy released = difference in binding energy between the products and reactants = 7.8 MeV – 2.2 MeV = 5.6 MeV.

51

(c) Why is this reaction unlikely to occur at room temperature?

Example continued:

At room temperature the reactants will not have enough kinetic energy to overcome the Coulomb repulsion between them to get close enough to fuse.

Summary

52

•The Nucleus (atomic & mass numbers)

•Binding Energy

•Radioactive Nuclei

•Alpha, Beta, and Gamma Radiation

•Half-life and Activity

•Absorbed Dose

•Spontaneous vs. Induced Nuclear Reactions

•Fission vs. Fusion