Atomic and Nuclear PhysicsAtomic and Nuclear Physics

Atomic structureAtomic structure

Atomic StructureAtomic StructureThe current model of atomic structure was not undestood until the 20th century.

● 1808 - John Dalton – new idea - the matter is made of atoms (tiny indivisible spheres)● 1897 – J. J. Thomson discovered that all matter contains tiny negatively‑charged particles.

→ Thomson’s “plum-pudding” model

– the atom was a positive sphere of matter and the negative electrons were

embedded in it

electrons(the plums)

positive matter (the pudding)

He showed that these particles are smaller than an atom. He actually found the first subatomic particle ‑ the electron.

● ● Ernest Rutherford got his students Geiger and Marsden to Ernest Rutherford got his students Geiger and Marsden to fire the fast moving fire the fast moving αα‑particles at very thin gold foil and ‑particles at very thin gold foil and observe how they were scattered.observe how they were scattered.

2 protons + 2 neutrons bound together into a particle identical to a helum nucleus; hence, it can be written as

– particle

RutherfordRutherford source of α: radioactive radon

4 42 2He or

1919 – Ernest Rutherford discovered proton1932 – Chadwick discovered neutron

► Scientists then set out to find the structure of the atom.

Expected result of Rutherford's experiment if the "plum pudding" model of the atom was correct.

Actual result: Most of the α‑particles passed straight through the foil, some are slightly deflected, as expected, but to his surprise a few were scattered back towards the source.

Rutherford said that this was rather like firing a gun at tissue paper and finding that some

bullets bounce back towards you!

Rutherford’s conclusion (1911):Rutherford’s conclusion (1911):▪ ▪ particle had a head-on collision with a heavier particle particle had a head-on collision with a heavier particle

▪ ▪ heavier particle had to be very small, since very few heavier particle had to be very small, since very few particlesparticles were bounced back. were bounced back.

▪ ▪ heavy particles must be positive (repulsion)heavy particles must be positive (repulsion)

→ nuclear (planetary) model of the atom:

Atom contains a small but very massive positive core which he called nucleus, surrounded by negatively charged electrons at relatively large distances from it.

The most suprising thing about this model is that the atom is mainly empty space!

Using this model Rutherford calculated that the diameter of the Using this model Rutherford calculated that the diameter of the gold nucleus could not be larger than 10gold nucleus could not be larger than 10-14-14 m. m.

which is why most α particles went straight through – any electrons would hardly impede the relatively massive’ high speed ).

Alpha particle (+2e) Gold nucleus

(+79e)rLoss in kinetic energy must be equal to gain in potential energy of α particle in the field of gold nucleus. Rutherford used an a source given to him by Madame Curie. The inital a energy was ~ 7.7MeV (KEinitial = 7.7 x 106 x 1.6 x 10-19 J = 12 x 10-13 J).

α paricle is brought momentarily to rest (“having climbed as far as it can up the electrostatic hill”) when changing direction of the motion. The speed and hence the kinetic energy is zero, all the energy is now electrostatic potential energy.

Calculate the distance of an alpha particle’s closest approach to a gold nucleus.

goldfinal final

Q = U = qV = 2e kinitialKE

rr ~ 3x10-14 m

Radius of gold atoms is ~ 3 ×10-10 m. So a nucleus is at least 10 000 times smaller than an atom. It is important to emphasise that this calculation gives an upper limit on the size of the gold nucleus; we cannot say that the alpha particle touches the nucleus; a more energetic might get closer still.

Nuclear AtomNuclear Atom no neutrons (AD 1911)

● Orbiting around nucleus in circles are the electrons. (if they were not orbiting but at rest, they would move straight to the nucleus; instead centripetal force is provided by the electrostatic attraction between electrons and nucleus.)  

Problems with Rutherford’s model:●  According to Maxwell, any accelerating charge will generate an EM wave ●  Electrons will radiate, slow down and eventually spiral in to nucleus. The end of the world as we know it.●  The solution was found in quantum theory. .

Bohr’s Model - atomic energy levels ● Electrons could only exist in certain orbits at specific levels (“discrete states”), called “stationary states.” ● Electrons in these stationary states do not emit EM waves as they orbit.● Photon is emitted when an electron jumps from excited state to a lower energy state.

Bohr’s Model - atomic energy levels

● Electrons could only exist in certain orbits (“discrete states”) called “stationary states.”

● Electrons in these stationary states do not emit EM waves as they orbit.

● Photon is emitted when an electron jumps from an excited state to a lower energy state (higher orbit to lower orbit). Energy of that photon is equal to the energy difference between two states. Ephoton = ΔE

● Albert Einstein: relationship between energy and frequency of a photon:

h = Planck's constant = 6.627x10-34 Js

● The frequency of emitted light (photon) is proportional to the change of energy of the electron.

EE hf fh

Efh

E1

ΔE = hf

... These energies naturally lead to the explanation of the hydrogen atom spectrum:

Bohr's model was so successful that he immediately received world-

wide fame. Unfortunately, Bohr's model worked only for hydrogen. Thus the final atomic model was

yet to be developed.

E2

E3

E4

E5

And it was. Soon enough. The modern model

The model we now accept is that there is a nucleus at the centre of the atom and the electrons do exist in certain energy levels, but they don’t simply orbit the nucleus. The probability of finding electron somewhere is given by wave function, resulting in some interesting patterns.

The result of this theory can be again visualised using very simple model, this time only energy level model. This model is not a picture of the atom but just represents possible energy of electrons.

1. A hot solid, liquid or gas at high pressure produces a 1. A hot solid, liquid or gas at high pressure produces a

continuous spectrum – all continuous spectrum – all λλ..

2. A hot, low-density / low pressure gas produces an emission-line spectrum – energy only at specific λ.

3. A continuous spectrum source viewed through a cool, low-density gas produces an absorption-line spectrum – missing λ – dark lines.

Thus when we see a spectrum we can tell what type of source we are seeing.

● ● Each element (Each element (atom/ionatom/ion)) produces a specific set of produces a specific set of absorption (and emission) lines.absorption (and emission) lines.

We call this the "We call this the "spectral signaturespectral signature" " or or ““fingerprintsfingerprints”” of an atom/ion. of an atom/ion.

● Allows the identification of elements across the galaxy and universe. (If we mapped it and can recognize it)

Emission Spectra

Absorption Spectra

Nuclear StructureNuclear Structure

● ● NucleonNucleonThe name given to the particles of the nucleus.The name given to the particles of the nucleus.

● ● NuclideNuclideA particular combination of protons and neutrons that form a A particular combination of protons and neutrons that form a nucleus. It is used to distinguish isotopes among nuclei.nucleus. It is used to distinguish isotopes among nuclei.

● ● Nucleon number (mass number) - ANucleon number (mass number) - AThe number of protons plus neutrons in the nucleus.The number of protons plus neutrons in the nucleus.

● ● Proton number - ZProton number - ZThe number of protons in the nucleus.The number of protons in the nucleus.

●● Isotopes

Nuclei (atoms) with the same number of protons but different numbers of neutrons.

● ● Neutron number - N (Neutron number - N (N = A – Z)The number of neutrons in the nucleus.The number of neutrons in the nucleus.

● ● Symbol for a nucleidSymbol for a nucleid

XAZ

73Li

Isotopes – Nuclei (atoms) of the same element differing in masses due to different numbers of neutrons (the same proton number, different nucleon number) .

▪ The existence of isotopes is evidence for the existence of neutrons, because there is no other way to explain the because there is no other way to explain the mass difference of two isotopes of the same element.mass difference of two isotopes of the same element.

▪ The same number of electrons – the same bonding - the same chemical properties

▪ Different masses – different physical properties

▪ Many isotopes do not occur naturally, and the most massive isotope found in nature is uranium isotope

▪ About 339 nuclides occur naturally on Earth, of which 269 (about 79%) are stable

▪ the current largest atomic number element, with atomic number 118, survived for less than a thousandth of a second

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click me!

The strong nuclear force

What holds the nucleus together?

Protons are positive, neutrons are neutral (they would drift apart if put them together), so if the electric force was the only force involved, you couldn’t

create a nucleus.

There has to be some other force that holds protons and neutrons together and it must be stronger than the electric force. Well, in a brilliant stroke of

imagination, physicists have named this force "the strong force."

Althoug the nuclear force is strong, nuclei do not attract each other, so that force must be very short range, unlike the electric force that extends forever.

The strong nuclear force was first described by the Japanese physicist Hideki Yukawa in 1935. It is the strongest force in the universe, 1038 times

stronger than gravitational force and 100 times stronger than the electromagnetic force.

It is the force which attracts protons to protons, neutrons to neutrons, and protons and neutrons to each other. That force has a very short range,

about 1.5 radii of a proton or neutron (1.5 x 10-14m) and is independent of charge and this is the reason the nucleus of an atom turns out to be so

small.

If the protons can't get that close, the strong force is too weak to make them stick together, and competing electromagnetic force can influence the

particles to move apart.

As long as the attractive nuclear forces between all nucleons win over the repulsive Coulomb forces between the protons the nucleus is stable. It

happens as long as the number of protons is not too high. Atomic nuclei are stable subject to the condition that they contain an adequate number of

neutrons, in order to "dilute" the concentration of positive charges brought about by the protons.

The most massive isotope found in nature is uranium isotope For more massive nuclei strong nuclear force can’t overcome electric

repulsion.

U23892

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Binding energy

● Energy (work) must be applied to a nucleus to break it up into separate, free particles. So, if work is done, then the energy must have

been transferred to nucleons.

● On the other hand the sum of the masses of the constituent free protons and neutrons is found to be more than the mass of original

nucleus.

● The only possible conclusion: energy is converted into mass ?????

Problem solved: Einstein’s Mass-Energy Equivalence Relationship:

In 1905, while developing his special theory of relativity, Einstein made the startling suggestion that

energy and mass are equivalent.

He predicted that if the energy of a body changes by an amount E, its mass changes by an amount m given by the equation

E = mc2 where c is the speed of light.

Everyday examples of energy gain are much too small to produce detectable changes of mass and cannot be used to

prove Einstein's equation.

● When nucleons bind together to form nucleus the mass of a nucleus is found to be less than the sum of the masses of the constituent protons and neutrons.

● Mass defect (deficit) - difference between the mass of a nucleus and the sum of the masses of its isolated nucleons

● A bound system has a lower potential energy than its constituent parts; this is what keeps the system together.The "mass defect" is therefore mass that transforms to energy according to Einstein's equation and is released in forming the nucleus from its released in forming the nucleus from its component particles.component particles.(heat, light, higher energy states of the nucleous/atom or other forms of energy).

● Binding energy (BE) - is therefore either the energy required to separate the nucleus into it individual nucleons or the energy that would be released in assembling a nucleus from its individual nucleons.

Calculations of binding energy

first find mass defect δ = Zmp + Nmn – Mnucleus

in unified atomic mass units (u)

Unified Atomic Mass Unit (amu abbreviated as u) – 1/12 of the mass of one atom of carbon-12 (6p+6n+6e).

● 1 u = 1.66053886 x 10-27 kg

usual way:

1u is converted into 1.492 x 10-10 J energy = 931.5 MeV:

E = (1.66053886 x 10-27 kg) (2.99792458 x 108 ms-1 )2 = 1.4924178992 x 10-10 J

1 electron volt = 1.60217646 × 10-19 joules-10

-10-19

1.4924178992×101.4924178992×10 J = MeV = 931.5 MeV1.60217646×10

binding energy: mass deficit converted into energy BE = δ c2

1 u of mass converts into 931.5 MeV → BE = δ(u) x 931.5 (MeV)

● Remember that periodic tables give atomic masses not nuclear masses. To get nuclear masses you have to subtract the masses of electrons in the

atom from atomic mass.

Example: Calculate the binding energy of iron Fe

From the periodic table: Z = 26 A = 54 mass = 53.940u (pure )

from data booklet: mproton = 1.007276u mneutron = 1.008665u melectron = 0.000549u δ = Zmp + Nmn – Mnucleus

δ = 26x 1.007276u + (54-26)x 1.008665u – (53.940u – 26x 0.000549u)

δ = 54.431796u – 53.925726u = 0.50607u

5426Fe

BE = δ(u) x 931.5 (MeV) BE = 0.50607 x 931.5 (MeV)

BE = 471.4 MeV

binding energy per nucleonbinding energy per nucleon - the binding energy the binding energy of a nucleus is divided by its mass numberof a nucleus is divided by its mass number

very often instead of atomic mass, nuclear mass will be given

(nuclear mass of Fe is 53.925726u)

BEA

for pure Fe it is 8.7 MeV/nucleon

If a nucleus has a large binding energy then it will require a lot of work to pull it apart – we say it is stable.

The binding energy curveThe binding energy curve

Graph of binding energy per nucleon

BE varies with mass BE varies with mass number;number;

BE increase as the BE increase as the mass (nucleon) number mass (nucleon) number

increases up to Fe. increases up to Fe.

Fe is most stable. Fe is most stable. After that it slightly After that it slightly

decreases.decreases.

In most cases it is about In most cases it is about 8 MeV8 MeV