01-Atomic n Nuclear Structure

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Atoms Ordinary matter is composed of atoms. An atom

consists of a tiny nucleus made up of protons and

neutrons, on the order of 20,000 times smaller than the

size of the atom. The outer part of the atom consists of

a number of electrons equal to the number of protons,

making the normal atom electrically neutral.

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Evolution of Theory for Matter

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Democritus

400 B.C.

Aristotle350 B.C.

JohnDalton1808

J.J.Thomson

1897

HantaroNagaoka

1904


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Models of Atom

Thomsons plum pudding model

Rutherfords model - the first

planetary model

Bohrs model

Paulis exclusion principle (1925)

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Rutherford Scattering

The Rutherford Atomic Model - 1911

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Distance Of Closest Approach

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Rutherfords ingredients:

Newtonian Mechanics (F = ma)

Coulomb Interaction=> Distance of closest approach

Coulomb repulsion between the a -particle (2+) and the Au nucleus (79+)

Let initial KE of a= PE at closest approach distance r.

KE (a) = 6 MeV

Therefore, r = 3.8x10-14 m = 38 fm = 38 fermi

r

qq

r

qq

F

21

0

2

21

0

4

1PE

;4

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Distance of closest approach

The faster an alpha particle is travelling, i.e. the more energy it has,

the closer it can get to the nucleus before being repelled away.

For any given initial energy, we can calculate how close the alpha

particle can get to the nucleus.

We call this the distance of closest approach.7

PE

r

a

Stops here

Distance of closest

approach


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Failures of Classical Atomic Model Unstable model, since an accelerated charge radiates i.e. will emit

light and therefore lose E

classical mechanics did not work for the planetary model - it

violated classical laws of electromagnetism

considerable problems with atomic spectra

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Bohr Model 1913 A countable number of stationary

states exist. (electrons in aselection of allowed orbit radii)

EM radiation emitted when

electron jumps/transitions between

states

Classical rules apply to stationary

states, but not during transitions

between states. Angular momentum occurs in

integer multiples of h/2.

i.e. mvr = nhence quantized.10

n=1

n=2

n=3

2 1h E E


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Quantized Energy States

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Hydrogen spectral series:

Patterns in the Spectra

10 10 0 10 00 10 000

(IR),8,7,61

5

11Pfund

(IR),7,6,51

4

11Brackett

(IR),6,5,41311Paschen

(UV),4,3,21

1

11Lyman

nm01097.0

light)(visible,5,4,31

2

11Balmer

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22

22

22

1

22

n

n

R

nn

R

nn

R

nn

R

R

n

n

R

n

n

n

n

n

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Energy Transfer Mechanisms

Excitation of the Atom

When a sufficient amount of energy is transferred to the atom,causing an electron to jump from the lower to higher energylevels, the atom is said to be excited.

Ionization of the Atom

When a sufficient amount of energy is transferred to the atom,causing an electron to be removed from the electric field of thenucleus, the is said to be ionized, and the negative electron

together with the remaining positively charged atom, is calledthe ion pair.

Excitation and ionization are the main mechanisms

through which energy is transferred from radiation to

matter

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Problem with Bohrs model and classical

mechanics

Could only predict correctly the energy levels of H.

The dual behavior of light (particle and wave) could

not be explained by classical mechanics

The approach of Bohr of mixing classical mechanicwith quantizing certain variables was suddenly

heavily used

other accurate predictions were made with newsemi-classical or relativistic models

Prelude to Quantum Mechanics 14


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Pauli principle: No two electrons in an atom

can be in the same state Quantization came naturally out of quantum mechanics

Four quantum numbers fully described the electron energylevels

Principal quantum number : n

Describes the orbital shells

n=1, 2 and 3 for K, L and M shells respectively

Corresponds to Bohrs angular momentum quantization

Azimuthal quantum number: l

Explains fine structure in spectrum (elliptic orbit)

l = 0, 1, 2, , n

Magnetic quantum number: m

Explains splitting of spectral lines in magnetic field - Zeeman Effect

m = [-l, l]

Intrinsic spin (angular momentum) of electron: s s = [-1/2, ]

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Neutron Chadwiick-1932.

The mystery particle (Y) has ~ proton mass but no chargeThe Neutron

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Nuclear Terminology Atomic number (Z) is the number of protons in the nucleus of an atom, and

also the number of electrons in a neutral atom

Nucleon: proton (Z) or neutron (N)

Nuclide: nucleus uniquely specified by the values of N & Z

Mass number (A) is the total number of nucleons in a nucleus (A=Z+N)

Isotopes: nuclides with the same protons (Z) e.g. 235U and 238U

Isotones: nuclides with the same neutrons (N) e.g. 2H (d) and 3He Isobars: nuclides with the same A

Atomic mass unit (u): one-twelfth of the mass of a neutral atom of 12C (six

protons, six neutrons, and six electrons). 1 u = 1.66 x 1027 kg = 931.5 MeV/c2

Atomic mass is the mass of a neutral atom and includes the masses of

protons, neutrons, and electrons as well as all the binding energy.

Nuclear mass is the mass of the nucleus and includes the masses of the

protons and neutrons as well as the nuclear binding energy, but does not

include the mass of the atomic electrons or electronic binding energy.

Radioisotopes: members of a family of unstable nuclides with a common

value of Z

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Nuclear Notation atomic mass = A

atomic number = Z = number of protons (+) = number of

electrons ()

AZ = number of neutrons (no charge) = N

e.g.238

U.A = 238 and U has Z = 92 protons. Therefore, 146 neutrons.

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Nuclear Units

SI units are fine for macroscopic objects like footballs but arevery inconvenient for nuclei and particles therefore nuclear unitsare used as:

Energy: 1 eV = energy gained by electron in beingaccelerated by 1V.

Mass: MeV/c2

(or GeV/c2

)1 MeV/c2= 1.78X10-30kg. 1 GeV/c2= 1.78X10-27kg.Or use Atomic Mass Unit defined by mass of 12C= 12 u

Momentum: MeV/c (or GeV/c)1 eV/c = e/c kg m s-1

Cross sections:1 barn =10-28 m2

Length: fermi (fm)

1 fm = 10-15m. 19


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Nuclear Units

Nuclear energies are very high compared to atomic processes,and need larger units

Nuclear sizes are quite small and need smaller units

Nuclear masses are measured in terms of atomic mass units

(amu, u) with the carbon-12 nucleus defined as having a massof exactly 12 amu. It is also common practice to quote the restmass energy E = mc2as if it were the mass. The conversion toamu is: 20

1amu = 1.6605 x 10-27kg = 931.5 MeV/c2


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Constituents of Atoms

The electrons, protons and neutrons which make up an atomhave definite charges and masses.

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Constituents of Atoms

While the charges and masses are precisely known, the sizing isnot. Our best information about the proton and neutron indicatesthat they are constituent particles. However we can attribute tothem a radius of about

1.2 x 10-15

meters = 1.2 fm

The electron is a fundamental particle which is apparently notmade out of any constituent particles.

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THE END

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01-Atomic n Nuclear Structure