Nuclear Physics and Radioactivity

AP Physics

Chapter 30

Nuclear Physics and Radioactivity

30.1 Structure and properties of the Nucleus

30.1 Structure and Property of the Nucleus

Nucleus is composed of two

particles

Proton – positive charge

Neutron – neutral

Together they are called nucleons

30.1

kgxm

Cxq

p

p

27

19

1067262.1

10602.1

kgxmn271067493.1

30.1 Structure and Property of the Nucleus

To present this information we use the symbol form

Z – number of protons (atomic number)

A – atomic mass (not average)

The number of Neutrons (N) is

Sometime written without the Z, as that information is redundant

30.1

XAZ

ZAN XA

30.1 Structure and Property of the Nucleus

Isotopes – the same element, but different numbers of neutrons or mass number

These isotopes would be

Not all isotopes are equally

common

C-12 is 98.9%

C-13 is 1.1%

Called the Natural Abundance 30.1

He52 He6

2 He72 He8

2

30.1 Structure and Property of the Nucleus

Masses of atoms are determined using a mass spectrometer

The mass is given

in unified atomic

mass units (u)

Carbon – 12 is

given the mass

of 12.000000u

30.1

ump 007276.1

umn 008665.1

30.1 Structure and Property of the Nucleus

Masses are often given in electron volts

This is derived from Einstein’s equation

Using the mass of a proton

And placing into Einstein’s equation

30.1

2mcE

ukgxprotonu

protonkgxu /1066054.1

/007276.1

/1067262.10000.1 27

27

JxsmxukgxE 102827 104924.1)/109979.2(/1066054.1

25.9311031.9106022.1

1104924.1 8

1910

cMeVeVx

Jx

eVJxE

Nuclear Physics and Radioactivity

30.2 Binding Energy and Nuclear Forces

30.2 Binding Energy and Nuclear Forces

The total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons

The difference is mass is

the binding energy

So for example the mass of

Helium 4 is 4.002603u

30.2

uxuxux enp 03297916.4)00054858.02()008665.12()007276.12(

uuu 0303761.0002603.403297916.4

MeVu

MeVu 30.28

1

5.9310303761.0

30.2 Binding Energy and Nuclear Forces

This is the energy needed to break apart the nucleus

To be a stable nucleus, the mass must be less than the parts

The binding energy per

nucleon is the total

binding energy divided

by A

30.2

30.2 Binding Energy and Nuclear Forces

Strong Nuclear Force – attractive force between all nucleons

Drops to essentially zero if the distance between the nucleons is greater than 10-15m

Occur by the exchange of a particle called a meson

Weak Nuclear Force – very weak, show in types of radioactive decay

30.2

30.2 Binding Energy and Nuclear Forces

30.2

Nuclear Physics and Radioactivity

30.3 Radioactivity

30.3 Radioactivity

Henri Becquerel (1896) uranium darkens photographic plates

Radioactive decay – unstable nuclei

fall apart with

the emission of

radiation

30.3

30.3 Radioactivity

Rays can be classified into three catagories

1. Alpha () – barely penetrates paper

2. Beta () – penetrates up to 3mm of aluminium

3. Gamma () – penetrates several cm of lead

30.3

Nuclear Physics and Radioactivity

30.4 Alpha Decay

30.4 Alpha Decay

An alpha particle is a helium nucleus

When an atom undergoes alpha

decay it loses 2 protons and 2

Neutrons

Reactions are written

30.4

HeRnRa 42

222862

22688

30.4 Alpha Decay

Parent nucleus – the original

Daughter nucleus – nucleus of new atom

Transmutation – change of one element into another

Basic form for alpha decay is

The alpha particle is ejected because it has a very large binding energy and is difficult to break apart

30.4

HeRnRa 42

222862

22688 HeNN A

ZAZ

42

420

Nuclear Physics and Radioactivity

30.5 Beta Decay

30.5 Beta Decay

Beta particle (-) – electron

Also produces an

antineutrino

Antineutrino – has no

charge and almost

no mass

The result of the decay is that a neutron becomes a proton 30.5

30.5 Beta Decay

For Carbon – 14 decay

Or the general form which would be

The electron does not come form the electron cloud, but from the decay of a neutron into a proton

It is identical to any other electron

30.5

veNC 147

146

veNN AZ

AZ

10

30.5 Beta Decay

Unstable isotopes with too few neutrons compared to their number of protons decay by emitting a positron

Positron – same mass as an

electron, positive charge

This is an example of an antiparticle (antimatter)

The decay pattern is30.5

e

veNN AZ

AZ

10

Nuclear Physics and Radioactivity

30.6 Gamma Decay

30.6 Gamma Decay

Gamma Ray – photon of

EMR

A nucleus can be in an

excited state like an

electron

When it drops down it emits a ray

Much larger than for electrons

For a given decay the ray has the same energy

30.6

30.6 Gamma Decay

The nucleus may enter an excited state by

Violent collision with another particle

The particle after a decay is often in an excited state

The equation can be

written

30.6

NN AZ

AZ 10

Nuclear Physics and Radioactivity

30.7 Conservation of Nucleon Number

30.7 Conservation of Nucleon Number

In radioactive decay all conservation laws are true

1. Energy

2. Linear Momentum

3. Angular Momentum

4. Electric Charge

Law of Conservation of Nucleon Number – the number of nucleons (protons or neutrons) remains the same, although they may change type

30.7

Nuclear Physics and Radioactivity

30.8 Half-Life and Decay Rate

30.8 Half-Life and Rate of Decay

Individual radioactive nuclei in a random process

Based on probability we can approximate the number of nuclei in a sample that will decay

Where is the decay constant30.8

tNN tNN Nt

N

30.8 Half-Life and Rate of Decay

The greater the decay constant, the greater the rate of decay

The more radioactive it is

The equation can be solved for N using calculus and we get

Where N0 is the initial number of nuclei present

N is the number remaining after time t

The number of decays per unit time is called the activity or rate of decay

30.8

teNN 0

30.8 Half-Life and Rate of Decay

Half-Life – the time it takes for half the original amount of parent isotope to decay (T½)

30.8

693.02ln

21 T

Nuclear Physics and Radioactivity

30.9 Calculations Involving Decay Rates and Half-Life

30.9 Calc. Involving Decay Rates and Half-Life

Carbon-14 has a half-life of 5730 yr. What is the activity of a sample that contains 1022 nuclei?

1 decay/s is called a becquerel (Bq)

30.9

693.0

21 T

21

693.0

T sx

yrsxyr/1083.3

)/10156.3)(5730(

693.0 127

Nt

N

sdecayxsxt

N/1083.3)10)(/1083.3( 102222

30.9 Calc. Involving Decay Rates and Half-Life

1.49mg of Nitrogen-13 has a half life of 600s.

a. How many nuclei are present?

b. What is the initial activity?

30.9

1623

60 109.6

0.13

10022.61049.1 x

g

nucleixgxN

sxT

/1016.1600

693.0693.0 3

21

sdecayxxsxNt

N/108)109.6)(/1016.1( 13163

30.9 Calc. Involving Decay Rates and Half-Life

1.49mg of Nitrogen-13 has a half life of 600s.

c. What is the activity after 3600s?6 half lives

If this had not been a perfect half life we would have used

30.9

1262113 1025.1))(108( xx

tet

N

t

N

0

Nuclear Physics and Radioactivity

30.10 Decay Series

30.10 Decay Series

Decay Series – a successive set of decay

30.10