nuclear physics simplified

Nuclear Physics

Particle physics

Properties of Nuclei

• Every atom contains an extremely dense, positively charged nucleus

• The nucleus is much smaller than the overall size of the atom, but contains most of its total mass


• Nucleus as a sphere– R depends on the total number of

nucleons (neutrons and protons) in the nucleus

– A is the nucleon number

R= R0A1/3

R0= 1.2x10-15m


•A is also the mass number in u–Proton mass and neutron mass ~ 1u–1u = 1.6605402 x 10 -

27kg

Nuclides and Isotopes

The masses of the building blocks of the nucleus:

mp= 1.007276u= 1.67263x10-27kg

mn= 1.008665u= 1.674929x10-

27kgme= 0.000548580u= 9.10939x10-

31kg


Z is the number of

protons in the nucleus

N is the number of neutrons

A is the sum


NuclideA single nuclear species having specific values of both Z and N

Same Z but

different N

Isotopes

Nuclear Binding Energy

• The energy that must be added to separate the nucleons

EB

• The magnitude of the energy by which the nucleons are bound together

EB

• (ZMH + Nmn - Z

M)c2

EB

A

MH= mass of protons and electrons mn= mass of neutron

Z M= mass of neutral atom c2= 931.5MeV/u

A

Example

• Deuterium has a mass number 2, an isotope of H. Its nucleus consists of a proton and a neutron bound together to form a particle called the deuteron. Deuterium has an atomic mass of 2.014102u. What is the binding energy of deuteron?

• 2.224MeV

Nuclear Binding Energy

• From the example, what is the binding energy per nucleon?• 1.112MeVper nucleon

Nuclear Force

• The force that binds protons and neutron together in the nucleus, despite the electrical repulsion of the protons

• An example of strong interaction

Nuclear Force

Does not depend on charge

1 It has short range (10-15m)

2

Interaction is within immediate vicinity

3 Favors binding of pairs

4

Nuclear Structure• Liquid Drop

Model• Proposed by

George Gamow• Suggests that

all nuclei have nearly the same density

Nuclear Structure• Nuclear forces

show saturation

• Nucleons on the surface of the nucleus are less tightly bound

• N is close to Z for small A

Nuclear Structure• Nuclear force

favors pairing of protons and neutrons

• Positive (more binding) if both Z and N are even

Nuclear Structure

• Summarizing these estimates into five terms:

• C1= 15.75MeV• C2= 17.80MeV• C3= 0.7100MeV• C4= 23.69MeV• C5= 39MeV

EB= C1A-C2A2/3-C3[(Z(Z-1))/A1/3]- C4[(A-2Z)2/A]±C5A-4/3

Z M= ZMH + Nmn – EB/c2

(Semi-empirical mass formula)

A

Example

• Considering the nuclide 62Ni28. a.) Calculate the five terms in the binding energy and the total estimated binding energy. b.) Find its neutral atomic mass using the semi-empirical mass formula

a. C1A= 976.5MeV -C2A2/3= -278.8MeV -C3[(Z(Z-1))/A1/3]= -

135.6MeV-C4[(A-2Z)2/A] = -13.8MeV+C5A-4/3 = 0.2MeV b. 61.925u

Nuclear Structure• The Shell

Model• Uses the

concept of filled shells and subshells and their relation to stability

Nuclear Structure• In atomic

structure, noble gases are stable

• A comparable effect occurs in nuclear structure

Nuclear Structure• An unusually

stable structure results when number of protons or number of neutrons is 2, 8, 20, 28, 50, 82, or 126

• MAGIC NUMBERS

Nuclear Stability & Radiation

• Radioactivity –The decay of unstable structures to

form other nuclides by emitting particles and electromagnetic radiation

–Alpha decay–Beta decay–Gamma decay


Alpha decay

Emission of alpha particle

4He nucleus

Emission occurs with nuclei that

are too large

N and Z, both decrease by 2, A decreases by

4


Beta minus decay occurs

When N/Z ratio is too

large

Neutral atomic mass is larger

than that of the final atom


Beta minus is

an electron

Emission involves

transformation of a neutron to

a:

Proton, electron, and

an antineutrino

N decreases and Z

increases by 1, A doesn’t change


Beta plus decay occurs

When N/Z ratio is too

small

Neutral atomic mass is at least 2 electron masses larger than that of the

final atom


Beta plus is a

positron

Identical to an electron but with

opp. charge

A proton is converted to a

neutron, a positron, and an

antineutrino

N increases and Z

decreases by 1, A remains

the same


Beta decay

Electron capture

Electron combines with a proton to form a neutron

and an antineutrino

The neutron stays in the

nucleus and the antineutrino is

emitted

N increases and Z decreases by

1, A remains the same


Bombardment of high-energy

particles and or by radioactive transformation

One or more photons are emitted from the nucleus

Gamma rays or gamma ray photons

(10keV – 5MeV)

Gamma ray decay

The element does

not change

Activities and Half-lives

• The decay rate• -dN(t)/dt

Activity

• Decay constant• Activity is prop. to the number

of radioactive nucleiλ

•=λN(t)-dN(t)/dt


• The number of remaining nucleiN(t)

• Decay constant• Activity is prop. to the number

of radioactive nucleiλ

•=N0e-λt N(t)


Units for activity– Ci or curie or Becquerel or Bq–1Ci= 3.70x1010Bq= 3.70x1010decays/s

Activities and Half-lives• Time required for

the no. of radioactive nuclei to decrease to half N0

Half life

•= 0.693/λT1/2

• =1/λ=T1/2/ln2=T1/2/0.693Tmean

Example

• The radioactive isotope 57Co decays by electron capture with a half-life of 272 days.

• A. find the decay constant and the lifetime

• B. if you have a radiation source containing 57Co, with activity 2.00μCi, how many radioactive nuclei does it contain?

• C. what will be the activity of your source after one year?

λ= 2.95x10-8/s Tmean= 3.39x107s

N(t)= 2.51x1012 nuclei

N(t)= 0.394N0 -dN(t)/dt= 0.788μCi

Radioactive Dating

A small proportion of the unstable 14C is present in CO2 in

the atmosphere

Plants that obtain their

carbon from this source contains the same prop.

When a plant dies, it stops taking carbon

14C β- decays to 14 N with a half-life of 5730 yrs. The

remaining 14C determines the age of the organism.

Biological Effects of Radiation


When radiation

pass through matter

They lose

energy

Break molecular

bonds

Create ions

Ionizing radiatio

n


Charged particles interact directly with the electrons in the

material

X rays and γ rays interact by the

photoelectric effect

Neutrons cause

ionization by:

Collisions with nuclei

Absorption by nuclei with subsequent

radioactive decay


Radiation dosimetry

The quantitative description of the

effect of radiation on living tissue

Absorbed dose

Energy delivered to the tissue per unit

mass

SI: J/kg, Gy(gray),

present: rad

1rad=0.01J/kg=0.01Gy

Biological Effects of RadiationRelative

Biological Effectiveness

(RBE)

The numerical factor describing

the different extents of

biological effects of different kinds

of radiation

Also called the Quality

factor

Xrays have the RBE of unit 1


Biological Effect

The product of the absorbed dose and

the RBE of the radiation

Biologically equivalent dose or equivalent

dose- SI: Sievert (Sv)

Equivalent dose (Sv)= RBE x

absorbed dose(Gy)


Biological Effect

More common unit, corresponding to the rad: Roentgen equivalent for man

(rem)

Equivalent dose (rem)= RBE x

absorbed dose(rad)

RBE units1Sv/Gy or 1rem/rad;

conversion 1rem= 0.01Sv


Radiation RBE ( Sv/Gy or rem/rad)

X rays and γ rays 1Electrons 1.0-1.5Slow neutrons 3-5Protons 10α particles 20Heavy ions 20

Example

• During a diagnostic x-ray examination, a 1.2kg portion of a broken leg received an equivalent dose of 0.40mSv. a) what is the equivalent dose in mrem? b)what is the absorbed dose in mrad and mGy? c)if the x-ray energy is 50keV, how many x-ray photons were absorbed? (1eV= 1.602x10-19J)

a. 40mremb. 40mrad; 0.40mGyc. 6.0x1010 photons

Example

• Calculate the total amount of energy (in joules) absorbed by a 750 g guinea pig, from an x-ray, at the lethal dose level of 4Sv.• 3 Joules

Example

• A typical cup of tea (250 mL) when consumed at 85oC will yield nearly 200 J of thermal energy to a human's stomach. What absorbed dose of radiation would be required to deliver the same amount of energy to a 60 kg human (by radiation)?

• 3.33 Gy

Nuclear Reactions

A process that alters the energy or structure or

composition of atomic nuclei.

Nuclear Reactions

Nuclear fissionA decay process

in which an unstable nucleus

splits into two fragments of

comparable mass

Nuclear ReactionsNuclear fission• Discovered by

the experiments of Otto Hahn and Fritz Strassman

• Bombardment of U with neutrons

Nuclear ReactionsNuclear fission• The resulting

radiation did not coincide with any of the know radioactive nuclide

• Lise Meitner found out its barium

Nuclear ReactionsNuclear fission• With Otto

Frisch, they discovered that U nuclei was splitting into 2 massive fragments called fission fragments

Nuclear ReactionsInduced fission• Fission resulting

from neutron absorption

• Rare Spontaneous fission occurs w/out initial neutron absorption

Nuclear Reactions: Fission

n

U-235

Ba-144

Kr-89

3n

Nuclear ReactionsNuclear Fusion• Occurs when 2

or more small light nuclei come together to form a larger nucleus

Nuclear ReactionsNuclear Fusion

1H1 + 1H1 2H1 + β+ + ve

2H1 + 1H1 3He2 + γ

3He2 + 3He2 4He2+1H1+1H1Proton-proton

chain

Nuclear ReactionsNuclear Fusion• 2 or more

nuclei must be w/in the range of nuclear force (approx. 2x10-15m)

Nuclear ReactionsNuclear Fusion• Thermonuclear

reactions• Proton-proton

reaction occurs at “only” 1.5x107K in the sun

• Cold fusion doesn’t require high temperatures

Reaction Energy

The difference between the

masses before and after the

reaction

When Q is pos., total

mass dec & the

total KE inc

EXOERGIC

Reaction

When Q is neg., total mass inc & the total KE

dec

ENDOERGIC Reaction

Q= (MA + MB – MC – MD) c2

Example

• When lithium (7Li) is bombarded by a proton, two alpha particles (4He) are produced. Find the reaction energy.

• Q= 17.35MeV

11H + 7

3Li 42He +

42He

H=1.007825u; Li= 7.016004u; He= 4.002603u

Example

• Calculate the reaction energy for the nuclear reaction represented below:

• Q= -1.192MeV

42He + 14

7N 178O

+ 11H

H=1.007825u; N= 14.003074u; He= 4.002603u; O=16.999132u

Nuclear Reactions

Nuclear Generator

nuclear physics simplified

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