Nuclear Physics

AP Physics B

Bequerl’s Ray…the beginning of Radiactivity

• French Scientist

• Uranium in a drawer

• Photographic paper

27

13 Al mass#!

Atomic #!“protons”

“Protons + neutrons”

29.1 Properties of Nuclei

A= mass #

Z=atomic #

N=neutron #

Symbols

A - Z = N

Before we begin to discuss the specifics of radioactive decay we need to be certain you understand the proper NOTATION that is used.

Nuclear Physics – Notation & Isotopes An isotope is when you have

the SAME ELEMENT, yet it has a different MASS. This is a result of have extra neutrons. Since Carbon is always going to be element #6, we can write Carbon in terms of its mass instead.

Carbon - 12 Carbon - 14

Einstein – Energy/Mass Equivalence In 1905, Albert Einstein publishes a 2nd major

theory called the Energy-Mass Equivalence in a paper called, “Does the inertia of a body depend on its energy content?”

Einstein – Energy/Mass Equivalence Looking closely at Einstein’s equation we see that he

postulated that mass held an enormous amount of energy within itself. We call this energy BINDING ENERGY or Rest mass energy as it is the energy that holds the atom together when it is at rest. The large amount of energy comes from the fact that the speed of light is squared.

Energy Unit Check

2

2

2

2

2

22

smkgm

smkgWE

smkgNmaF

NmJouleFxWsmkgJoulemcE

net

B

×=××==

×=→=

=→=

×=→Δ=

29.2 Binding Energy

E bind = Δmc2

Because mass = energy ; unbound nucleons will sponatneously bind together.

• Binding energy = rest energy

Ebind = (munbound – mbound ) c2

Mass Defect

The nucleus of the atom is held together by a STRONG NUCLEAR FORCE. The more stable the nucleus, the more energy needed to break it apart. Energy need to break to break the nucleus into protons and neutrons is called the Binding Energy Einstein discovered that the mass of the separated particles is greater than the mass of the intact stable nucleus to begin with. This difference in mass (Δm) is called the mass defect.

12

6 C

Atomic mass unit (u) is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state,[2] and has a value of 1.660538921(73)×10−27 kg.[3]

Proton mass = 1.67 x 10 -27 kg , Thus the charge due to mass for a proton = 938.3 MeV Particle kg u MeV/c2

Proton 1.67 x 10 -27 1.007276 938.3 neutron 1.675 x 10 -27 1.008665 939.6 electron 9.109 x 10 -31 0.000549 0.5110

u = 931.5 MeV / c2

29.2 Binding Energy

Δm = Z (atomic mass unit of proton ) + N (atomic mass unit of neutron) -atomic mass

1.Determine the binding energy of

Knowns: Z=10 A=20 Ne= 19.992435 mn = 1.008665 u mp= 1.00728u

Δm= 10 (1.00728u)+10(1.008665u)- 19.992435u

Δm= 0.17246 now….

E bind = (0.17246u) (931.5 MeV / u )

E bind = 160.6 Mev

20 10

Ne

Mass Defect – Example

Radioactivity When an unstable nucleus releases energy and/or

particles.

Radioactive Decay There are 4 basic types of

radioactive decay n  Alpha – Ejected Helium n  Beta – Ejected Electron n  Positron – Ejected Anti-

Beta particle n  Gamma – Ejected Energy

You may encounter protons and neutrons being emitted as well

np

eeHe

10

11

00

01

01

42

γ

−

Alpha Decay

HeUPu 42

23692

24094 +→

Alpha Decay Applications

?42

24195

AZHeAm +→

Americium-241, an alpha-emitter, is used in smoke detectors. The alpha particles ionize air between a small gap. A small current is passed through that ionized air. Smoke particles from fire that enter the air gap reduce the current flow, sounding the alarm.

238

92 U 234

90 Th 4

2He• Helium is the alpha particle

Rules for nuclear decay

1. Total atomic # on right =# on left

2. Mass on right = mass on left

Decay produces an electron!

14

6

14

7 N 0

-1eC

Beta Decay

AceRa 22889

01

22888 +→−

There aren’t really any applications of beta decay other than Betavoltaics which makes batteries from beta emitters. Beta decay, did however, lead us to discover the neutrino.

Beta Plus Decay - Positron

ThePa 23090

01

23091 +→

Isotopes which undergo this decay and thereby emit positrons include carbon-11, potassium-40, nitrogen-13, oxygen-15, fluorine-18, and iodine-121.

Beta Plus Decay Application - Positron emission tomography (PET)

Positron emission tomography (PET) is a nuclear medicine imaging technique which produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Images of tracer concentration in 3-dimensional space within the body are then reconstructed by computer analysis.

Beta decay has energy left over!

12

5

12

6 C + 0

-1 e+ vB 12C 6

12

6 C

+

antineutrino

STEP ONE

STEP TWO

γ

Gamma Decay

γ0024094

24094 +→ PuPu

Gamma Decay Applications Gamma rays are the most dangerous type of radiation

as they are very penetrating. They can be used to kill living organisms and sterilize medical equipment before use. They can be used in CT Scans and radiation therapy.

Gamma Rays are used to view stowaways inside of a truck. This technology is used by the Department of Homeland Security at many ports of entry to the US.

How does a Geiger Counter Work?

n  Geiger counters are used to detect ionizing radiation, usually beta particles and gamma rays, but certain models can detect alpha particles. An inert gas-filled tube (usually helium, neon or argon with halogens added) briefly conducts electricity when a particle or photon of radiation makes the gas conductive. The tube amplifies this conduction by a cascade effect and outputs a current pulse, which is then often displayed by a needle or lamp and/or audible clicks.

The “clicking” is simply the amplification of the current on a speaker…it could have any sound (like a synthesizer that sounds like a trumpet etc….) �

A simple relationship exists between the number N of atoms in a sample and the number that will decay in a short period of time

A half life (T 1/2 )is the time it takes for half the sample to give off its radioactive nuclei.

Lambda is

the decay

constant!

T 1 / 2 =0.693λ

Is also called activity

€

N = N0e−λt ΔN

Δt

No

1/2No

1/4No

1/8No

T 1/2 2T 1/2 3T 1/2 Iodine decay

No

1/2No

1/4No

1/8No

T 1/2 2T 1/2 3T 1/2 Iodine decay

A 100g radioactive sample decays to 45g in 2.5 yrs. What is the half life of this substance? a)Find the 2nd and third half lifes

a)  N= N0e -λt

b)  so 45 = 100 -λ2.5

c)  lambda = .319 yrs-1

d) 

e)  2.17 yrs

T 1 / 2 =0.693λ

No

1/2No

1/4No

1/8No

T 1/2 2T 1/2 3T 1/2 Iodine decay

The half life of the radioactive radium (226Ra) nucleus is 5x1010 secs. A sample contains 3.0 x 10 16 nuclei.

•  What is the decay constant for this reaction?

T 1 / 2 =0.693λ

a)

1.39x10-11 1/s

Significant Nuclear Reactions - Fusion

nHeHH 10

42

31

21 +→+

nuclear fusion is the process by which multiple like-charged atomic nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy.

Fusion Applications - IFE In an IFE (Inertial Fusion Energy) power plant, many (typically

5-10) pulses of fusion energy per second would heat a low-activation coolant, such as lithium-bearing liquid metals or molten salts, surrounding the fusion targets. The coolant in turn would transfer the fusion heat to a power conversion system to produce electricity.

Significant Nuclear Reactions - Fission

Nuclear fission differs from other forms of radioactive decay in that it can be harnessed and controlled via a chain reaction: free neutrons released by each fission event can trigger yet more events, which in turn release more neutrons and cause more fissions. The most common nuclear fuels are 235U (the isotope of uranium with an atomic mass of 235 and of use in nuclear reactors) and 239Pu (the isotope of plutonium with an atomic mass of 239). These fuels break apart into a bimodal range of chemical elements with atomic masses centering near 95 and 135 u (fission products).

energynKrBaUn +++→+ 10

9236

14156

23592

10 3

Fission Bomb One class of nuclear weapon, a fission

bomb (not to be confused with the fusion bomb), otherwise known as an atomic bomb or atom bomb, is a fission reactor designed to liberate as much energy as possible as rapidly as possible, before the released energy causes the reactor to explode (and the chain reaction to stop). A nuclear reactor is a device in

which nuclear chain fission reactions are initiated, controlled, and sustained at a steady rate, as opposed to a nuclear bomb, in which the chain reaction occurs in a fraction of a second and is uncontrolled causing an explosion.