Physics...HSC Physics Course Notes Vithushan Gandhiji Electromagnetic Spectrum Maxwell’s Equations...

Physics Vithushan Gandhiji

Table of ContentsElectromagnetic Spectrum III

Maxwell’s Equations III

Propagation of EM Waves III

Speed of Light IV

Galileo Galilei IV

Ole Romer IV

James Bradley IV

Modern Day Values V

Hippolyte Fizeau & Leon Foucault V

Definition of a Metre and a Second V

Spectroscopy VI

Physics Behind Spectroscopy VI

How a Spectroscope Works VI

Stellar Applications of Spectroscopy VI

Surface Temperature VI

Rotational & Translational Velocity VII

Density VII

Chemical Composition VIII

Light: Wave Model VIII

Newton’s Corpuscular Model VIII

Huygen’s Wave Model IX

Polarisation and Malus’ Law X

Light: Quantum Model XI

Black-body Radiation XI

Light and Special Relativity XII

Einstein’s Two Postulates XII

Experimental Evidences for Einstein’s Two Postulates XII

Muon Decay XII

Atomic Clocks, Hafele-Keating Experiment XIII

Michelson-Morley Experiment XIV

Positron Emission Tomography XV

From the Universe to the Atom XVI

The Big Bang Theory XVI

Evidences for the BBT XVI

Evidences for an Expanding Universe XVII

HSC Physics Course Notes Vithushan GandhijiEmission, Absorption and Continuous Spectra XVII

Emission Spectra XVII

Absorption Spectra XVII

Continuous Spectra XVIII

Classifying Stars Using Stellar Spectra XVIII

Nucleosynthesis Reactions in Main Sequence & Post-Main Sequence Stars XVIII

Proton-Proton Chain XVIII

CNO Cycle XIX

Post-Main Sequence Stars XIX

Early Experiments Examining the Nature of Cathode Rays XIX

Cathode Rays - Waves or Particles? XIX

Thompson’s Plum Pudding Model XX

Implications of Thompson’s Charge-to-Mass Ratio Experiment XX

Millikan’s Oil Drop Experiment XX

Geiger-Marsden Experiment XXI

Rutherford’s Model of the Atom XXI

Chadwick’s Discovery of the Nucleus XXI

Limitations of the Bohr and Rutherford Model of the Atom XXII

Limitations of Rutherford’s Model of the Atom XXII

Limitations of Bohr’s Model of the Atom XXII

Experimental Evidence for De Broglie’s Matter Waves XXII

Schrödinger’s Contribution to Quantum Mechanics XXII

Schrödinger’s Cat Thought Experiment XXIII

Alpha, Beta and Gamma Decay XXIII

Properties of Alpha, Beta and Gamma Radiation XXIII

Uncontrolled and Controlled Fission Chain Reaction XXIII

Controlled Fission Chain Reactions XXIV

Accounting For Energy Released During Fusion XXIV

Binding Energy XXIV

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HSC Physics Course Notes Vithushan Gandhiji

Electromagnetic Spectrum

Maxwell’s Equations 1. Gauss’ Law for electricity and magnetism.

- The net electric flux through a Gaussian (closed) surface is proportional to the net electric

charge within that surface.

- Magnets do not exist as monopoles. This implies if any magnetic field lines leave a

Gaussian surface, they must also enter it, therefore the net magnetic flux through the

surface must be zero.

2. Faraday’s Law of induction. Maxwell formulated Faraday’s ideas mathematically that the rate of

change of magnetic flux is directly proportional to the strength of the induced emf and hence is

related to the strength of the electric field produced by the induced current.

3. Ampere’s Circuital Law. A magnetic field is produced by a changing electric flux. In essence, a

changing electric field produces a changing magnetic field. In order to make the equation work for

situations where the currents and charges were variable, he had to add a new element called the

“displacement current” which represents a slight separation of electrons from their atoms in a

material when a varying electric field passes through it. This required the use of the permeability

and permittivity of free space. It allowed the equation to describe both magnetic and

electric fields changing in space as sine waves and so permitted electromagnetic radiation.

According to the wave equation, . This meant in order to find the velocity of light, all

that needed to be predicted were the permittivity and permeability of free space.

Propagation of EM Waves To produce an electromagnetic wave, an oscillating electric charge is required, by Maxwell[s 4th law,

Ampere’s Circuital Law. As a changing electric field produced by an oscillating electric charge induces a

changing magnetic field. And by Maxwell’s 3rd law, Faraday’s Law of induction, a changing magnetic

will induce an emf which induces a current that produces an electric field. By unifying electricity and

magnetism, Maxwell predicted that this would continue on and on in a series and hence results in the

ΦE =qϵ0

ΦB = 0

ϵ = − NΔΦB

Δt

(μ0) (ϵ0)

c =1

μ0ϵ0

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self-propagation of electromagnetic waves at the speed of light.

Speed of Light

Early Day Values

Galileo Galilei

Galileo and his assistant both carried a lamp to the tops of approximately 1 km apart hills. He used a

clock which was used to evaluate a value for time off the basis of how much water or sand was poured

out in the time interval. He uncovered his lantern at the same time he uncovered his clock and after his

assistant saw the light let out from Galileo’s lantern, he uncovered his lantern. After Galileo saw his

assistant’s lantern, he stopped the timing. After his calculations, he determined that the speed of light is

at least 10 times faster than the speed of sound.

Ole Romer

The fault in Galileo’s measurements were that the time

taken for light to cover the distance was too small to be

measured with the equipment available, so Romer

improved his method by extending the distances to stellar

distances, in this case from Paris’ observatory to Jupiter’s

moon Io. Romer used the fact that Jupiter’s moon Io

would emerge from behind Jupiter at different times

depending on the location of Earth in its orbit. At one

point in Earth’s orbit A, Romer found the period of each

orbit by measuring 4 successive appearances and

disappearances of Io from behind Jupiter, giving him an

average value of 42 hours, 28 minutes and 31.25 seconds.

Then Romer observed Io 26 orbits of Jupiter after at B and found the difference in Io’s recorded

period to be 15 minutes greater. Using the best measurements for the diameter of Earth’s orbit,

scientists calculated the speed of light to be .

James Bradley

While trying to measure the parallax of stars due to Earth’s rotation, he instead discovered the

phenomenon of stellar aberration. This effect is the slight changes in the positions of stars overhead

depending on the time of year, he noticed that light appeared to be arriving further in front the faster

you were moving and since this effect would not exist if light traveled infinitely fast, Bradley observed

that light does have a finite speed which he calculated to be .

2.1 × 108 m s−1

3 × 108 m s−1

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Modern Day Values Hippolyte Fizeau & Leon

Foucault

Fizeau had a disc with slots cut into them at regular intervals attached to a gear system which allowed

for high speed rotation, which he used to shine a light through. He then placed a mirror 8 km away to

reflect the light back through the slots when rotated slowly. As he increased the speed of the disc, it

started to appear transparent. As he continued to increase the speed, he reached a speed where light no

longer came back through the disc, losing its transparency. By the time light had returned to it from the

16 km distance, the disc had rotated slightly to block the light. Using the rotation rate of the disc and

the fraction of the circumference needed for the disc to block the returning light, he could determine

the time that it took light to travel 16 km. Then using , he was able to calculate the speed of light

to be .

Leon Foucault improved on Fizeau’s method by using a rotating mirror instead of a rotating

disc. The returning light was reflected at an angle determined by how far the mirror had rotated in its

journey. By 1862, he refined his measurements and determined the speed of light to be

.

Definition of a Metre and a Second Given that the speed of light was constant at , it was determined that the speed of

light was a precise standard that every one could agree on in the definition of a metre and a second.

One metre was defined by how far light travels in seconds.

The second was precisely defined as the time taken for 9192631770 of the energy transitions of

Caesium-133 atoms.

v =st

3.13 × 108 m s−1

2.98 × 108 m s−1

c = 299792458 m s−1

1299792458

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Spectroscopy

Physics Behind Spectroscopy

Every electron surrounding an atom has an exact energy level. Light also has a fixed energy level,

determined by . When photons interact with ground state electrons, the electrons move up

energy levels, however they are unstable due to Maxwell’s equations which say that moving charges

generate electromagnetic radiation. This causes the electron to fall back from an excited state to a

ground state, releasing a photon of the exact energy required to move it to its particular shell or level.

For single atoms, there is a set of energy transitions that its electrons may undergo, acting like a

signature, and every element has its own unique set, due to the fact that each element has a different

number of protons, so the electrostatic force of each nucleus is different, leading to different energy

levels, subshells and orbitals.

How a Spectroscope Works

Spectroscopes typically use a prism in order to separate

light into its constituent wavelengths by refracting

different wavelengths of light at deviating angles from

each other towards the normal as it enters a new

medium, causing light to be dispersed. To identify the

absorption spectrum of a substance, its gas is placed

near the incandescent light source, causing the different

elements within the gas to absorb different frequencies

of light. The photons which are re-released by the

electron are emitted radially, in all directions, so there is

only a small fraction of the re-emitted light which travel

in the same directions as the photons, which does not

cause an observable difference in its spectrum. This

appears as black lines on a continuous spectrum, called

absorption lines. These absorption lines can then be compared with the absorption lines of different

elements to evaluate the constituent elements of the gas.

Stellar Applications of Spectroscopy Surface Temperature

A star is a black body, emitting all frequencies of electromagnetic radiation from their cores, and as

with any incandescent body its peak wavelength indicates its temperature. Therefore, its surface

temperature can be determined by its apparent colour. Hotter stars emit higher frequencies of light and

hence have a colour towards the blue end of the visible spectrum. Cooler stars emit lower frequencies

of light and hence have a colour towards the red end of the visible spectrum. Some stars are so hot

E = h f

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that they emit wavelengths of light that are so low, they do not fit within the range of the visible

spectrum of light and hence are invisible to the naked eye.

Rotational & Translational Velocity

The relative velocity of a star that is approaching or receding the observer, called the radial velocity, can

be calculated by determining the red or blue shifts exhibited in its spectrum, due to the Doppler effect.

When a star is rotating, it results in the side

approaching the observer being blue shifted while the side

receding the observer appears to be red shifted. This results

in a simultaneous expansion of the absorption lines to either

side of it, causing a broadening in its spectrum. By

measuring the amount of broadening, along with the

estimate of the size of the star can lead to the calculation of

the rotational velocity of the star.

To determine the translational velocity of a star, a vector sum of the radial and tangential

velocity is taken.

Density

Lower density stellar atmospheres produce sharper, narrower spectral lines due to the motion of the

atoms and ions that are absorbing the radiation and producing the lines. Particles in lower density

(380 − 740 n m)

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atmospheres have to travel further before each collision, causing sharper absorption lines. As giant stars

have less gravity near the surface, the pressure of the gases near the surface is lower and hence the

absorption spectrum being produced is finer.

Chemical Composition

Photons are absorbed by gases in a star’s atmosphere and then re-emitted in all directions. Stars may

have many elements in their atmosphere, each producing its own characteristic spectral lines. Matching

the absorption lines of those found in a star’s spectrum with the absorption lines of different elements,

allows scientists to identify which elements are present in a star’s atmosphere and hence determine their

chemical composition. The relative intensity of the absorption lines indicates the abundance of that

element in the star’s atmosphere.

Light: Wave Model

Newton’s Corpuscular Model He proposed that light consists of small particles, these particles have mass and obey the laws of

physics and are so small that when two beams cross they do not scatter.

Reflection was explained by analogising a light particle with a particle such as a ball bearing

undergoing an elastic, frictionless collision against a smooth surface, which would preserve the angle of

incidence towards the normal of the surface when being bounced off with an angle of reflection.

Rectilinear propagation served as Newton’s evidence for his theory. If light travelled in

straight lines, it would make sharp shadows which he observed to be true.

Refraction is explained by Newton as particles of light

being attracted to particles of matter. A particle already within

a refractive medium would experience no net force as it would

experience attractions equally in all directions. However, when

it approaches a denser medium, from an oblique angle the

short range attractive forces from the particles in that medium

would cause a net force to accelerate the light particle in the

direction towards the normal resulting in a parabolic trajectory.

The component of the light particle’s velocity parallel to the

interface would be unaffected by the net force. This matched

observations made.

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Observations were made that part of the light sometimes reflected during refractions. Newton

explained this using his Theory of Fits, where he proposed that some particles that could fit between

atoms would be refracted and the others would be reflected.

Colours during dispersion were explained by Newton as different coloured light particles

having varying masses giving them more or less inertia, causing them to accelerate at different amounts

to the normal, resulting in the deviation of colours as light enters a new medium causing it to disperse.

Polarisation occurs when light enters a polarised surface at different angles causing varying

intensities of light. For polarisation to occur, the light particles could not be spherical in shape. When

this was observed, Newton proposed that light particles must have sides although the exact shape was

hard to visualise.

Debunking of Newton’s Theory

Foucault’s method involved shining a light to a rotating mirror which reflected it towards a tube filled

with water. He also used a reference of light in air by using the same method but omitting the rotating

mirrors. When Foucault conducted his test of measuring the speed of light in different optical media,

according to Newton’s predictions, light should travel faster in water than air as it is optically denser

causing the light travelling through the water to be deflected less than light travelling through air. This

was proven false when he observed the inverse was true, as the angle of deviation was smaller in air

than water, proving light to travel faster in air rather than water.

Huygen’s Wave Model Reflection occurs when wavefronts meet a surface at the angle of incidence. This creates new wavelets

associated with the wavefront leaving the surface at the angle of reflection.

Refraction of light was proposed by Huygen’s to cause light to bend towards the normal of an

optically denser medium, obeying Snell’s Law, whilst causing it to slow down in the new medium. The

observation that light partially refracts and reflects when there is a change in velocity of mechanical

waves strongly supported Huygen’s theory. This effect strongly depends on the angle of incidence and

is most pronounced when the velocity of the waves are increased.

Diffraction is the bending of light as it passes the edge of an object or goes through a gap.

The amount of diffraction increases as the length of the gap approaches the wavelength of the wave.

Once the wavelength of light was discovered to be very small between 400 and 700 nm, this solved

Huygen’s issue with rectilinear propagation, as with such small wavelengths, very little diffraction would

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Polarisation and Malus’ Law Polarisation can be described as “filter” of waves by their orientation in space. If a polarising lens has

lines travelling at then the light striking that lens will be polarised, so that only specific waves pass

through.

Malus’ Law states a relationship of the angle between the axes of the polariser and analyser.

It is known that,

Equating,

Unpolarised light consists of rays that oscillate in every plane possible. Hence, when passed

through a polariser, only the respective components of each ray aligned with the axis of the polariser

will be able to pass through, resulting in an exact halving in the rays of light that leave the polariser.

This means that the intensity of the light will also be halved, i.e.

0∘

θ

A2 ∝ I

I ∝ (A0cosθ)2

A2 = A2o cos2θ

I = I0 cos2θ .

I =12

I0 .

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Light: Quantum Model

Black-body Radiation A black body is an ideal surface that completely absorbs all wavelengths of electromagnetic radiation

that falls on it, while also perfectly re-emitting all absorbed radiation. A perfect black body will absorb

and emit all radiation supplied to it. Though, we don’t really have these in reality.

Examples of black bodies include an oven, stars, old-fashioned tungsten filaments of light

bulbs, etc. The radiation emitted by a heated object follows a distribution when graphing wavelength

against intensity, showing that the radiation emitted is a continuous spectrum. The shape of the curve

depends purely on its temperature.

“As temperature increases, decreases.” This relationship is given by Wein’s Law stated originally as,

Where is a constant, , called Wein’s displacement constant. is temperature in

Kelvins.

λmax

λmax =bT

b 2.898 × 10−3 m K T

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Light and Special Relativity

Einstein’s Two Postulates 1. The laws of physics are the same in all inertial frames of reference.

2. The speed of light has the same value, , in all frames of reference.

Time dilation,

Length contraction,

Mass dilation,

Momentum dilation,

Energy mass equivalence,

Experimental Evidences for Einstein’s Two Postulates

Muon Decay Muons are particles that are produced as a result of the bombardment of cosmic rays in the

upper atmosphere. They travel close to the speed of light and have an average lifetime of .

Given the speed with which they travel at and the distance of the atmosphere, most of them would

decay before reaching the surface. The Rossi-Hall experiment involved measuring the number of

muons that strikes a detector placed on top of a mountain top and comparing it with the number of

muons that strikes a detector placed on a lower level. The results showed that far more muons survived

the journey through the atmosphere than predicted without time dilation. The muons were travelling so

fast relative to the Earth that they decayed at a much slower rate than observed for observers on

Earth compared to if they were at rest in the laboratory.

c

t =t0

1 − v2

c2

.

ℓ = ℓ0 1 −v2

c2.

m =m0

1 − v2

c2

.

ρ =ρ0

1 − v2

c2

.

E = m c2 .

(μ−)2.2 μs

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The number of muons decaying between detector 1 and 2, was observed to be far less,

suggesting that the time passing in the muon frame of reference was much slower than the time passing

on Earth-based clocks.

Atomic Clocks, Hafele-Keating Experiment

In October 1971, Richard Keating and Joseph Hafele sent atomic clocks on commercial jets twice

around the world, one flown east ward and one west ward. They were then compared with Earth-frame

clocks and the results showed that the times shown by the clocks differed from that of the stationary

clocks relative to Earth, proving the predictions of special relativity.

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Michelson-Morley Experiment

The Michelson-Morley experiment shone a monochromatic source of light at a half-silvered mirror

positioned at an angle such that, any reflected light would be orthogonal to the ray of incidence. In the

setup, part of the beam would travel through the mirror where it would reflect across a mirror .

Some of the light reflected across would then, again, reflect off and travel to the receiver.

Part of the beam would reflect across and reflect again at travelling back through and into

the receiver. Due to the orthogonality of the beams, any rotation of the setup would still result in a

component of one of the beams being parallel to the supposed medium of the “luminiferous ether”.

This means that as the angle of rotation is changed, one side and then the other will become

more and more parallel to the ether resulting in a varying disturbance of the beams, resulting in a

changing interference pattern at the receiver where the beams are collected.

Their methods failed to prove the existence of the luminiferous ether. This is in accordance

with Einstein’s first postulate which states that the speed of light is constant in any frame of

reference, proving the predictions of Einstein’s special relativity.

M3 M2

M2 M3

M3 M1 M3

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Positron Emission Tomography Positron emission tomography uses the radiation emitted under the particle-antiparticle annihilation in

medical physics for imaging techniques used in PET scans. It specifically utilises the electron-positron

annihilation,

In medical imaging, certain radioactive atoms are attached to glucose molecules which are then

injected into the body. These radioactive atoms then undergo radioactive decay, in which positrons are

produced. Since the surroundings are filled with an abundance of electrons, as soon as a positron is

emitted, it will strike an electron producing gamma rays. Parts of the brain which are more active will

have a higher intensity of gamma rays produced, as glucose consumption in that region would be

greater. Hence, a ring shaped detector is used in PET scans to collect the fired gamma rays. Since the

gamma rays are fired in opposite directions, they will form a line. Each pair is associated with a line.

This method helps scientists locate tumours in the body by looking at hotspots, identifying a cancer,

ischaemia or figuring out which parts of the brain are most active.

01e + 0

−1e → 2γ .

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From the Universe to the Atom

The Big Bang Theory According to the BBT, all there was at the beginning of time was energy. This energy spread out from a

highly concentrated point called the singularity. The temperature was very high, as the energy

distributed through vaster distances, in any other region the temperature was significantly lower than

that of the singularity. Particles eventually started form from energy, so do the forces mediated by the

field particles. However, at very high temperatures they became destroyed. Once temperatures started

to cool, particles became more stable and began to combine, eventually allowing conditions for atoms

and molecules to form. The energy from the singularity is all the energy in the universe, currently

distributed in matter and radiation.

Evidences for the BBT According to predictions, any any residual gamma rays from the BBT would be seen in every direction,

but the wavelengths would be extremely stretched out due to the expansion of the universe and hence

would be observable now as microwaves, corresponding to a temperature of around 3 K. In 1965,

Robert Wilson and Arno Penzias measured this radiation for the first time, Satellites launched by

NASA and the European Space Agency have been able to measure the cosmic background microwave

radiation (CMBR).

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Evidences for an Expanding Universe By comparing wavelengths of hydrogen from other nebulae to those in laboratories, the relative speed

of the nebulae relative to the earth could be found, which Hubble deduced from the calculations that

they are moving much faster than any known object within our own galaxy and that the further away a

galaxy was the faster it was moving relative to the earth

Emission, Absorption and Continuous Spectra Emission Spectra

An emission spectrum is produced when low pressure gas atoms are heated or excited by other means

such as an electric field. The electrons absorb the energy and jump to higher energy levels. The excited

atom then

releases this energy as a photon when falling back to its ground state, the frequency determined by

. The release of the absorbed energy only occurs at certain frequencies hence the observed

spectrum has bright lines against a dark background.

Absorption Spectra

An absorption spectrum is produced when electrons in an atom, ion or molecule of a star absorb

radiation at set wavelengths. The absorbed wavelengths are determined by the difference in energy

levels that the electron jump between. The absorbed radiation is re-emitted but only very few in the

E = h f

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same original direction. Because a star produces a continuous spectrum due to its blackbody radiation,

the absorbed wavelengths appear as dark lines against a continuous spectrum.

Continuous Spectra

Continuous spectra are produced by black bodies at very high temperatures such as the tungsten

filament in an incandescent globe. The peak temperature emitted by most of the surface however, there

are other emissions from the surface at different at higher and lower energies, hence there is a spread

of energies. The typical spread is shown on a Planck curve. As the temperature of the body increases,

the peak wavelength becomes shorter, known as Wien’s Displacement Law,

The core of a star, a region of dense nuclei produces a continuous spectrum.

Classifying Stars Using Stellar Spectra Key features used to classify starts include the appearance and intensity of spectral lines, the relative

width of certain absorption lines, and the wavelength at which peak intensity occurs. The apparent

colour of a star is determined by its surface temperature.

The strongest Balmer series absorption for stars is class A, at 10 000K, with the hottest stars (class O)

having no discernible Balmer series due to the lack of hydrogen due to ionisation. Cooler stars have a

weak Balmer series (class M)

Nucleosynthesis Reactions in Main Sequence & Post-Main Sequence Stars

Proton-Proton Chain

Two protons undergo fusion to form deuterium, whereby the proton decays into a neutron emitting a

positron,

The deuterium atom now undergoes fusion to form helium-3 by reacting with a proton. Most of the

energy is released as gamma rays,

Finally, two helium-3 nuclides undergo fusion to form helium-4, which is stable. Two protons are

released back within the star.

Hence, the net equation follows as,

λmax =b

Tmax

11H + 1

1H → 21H + e+ + v

21H + 1

1H → 32He + γ

32He + 3

2He → 42He + 1

1H + 11H

41H → 4

2He + 2e+ + 2v + 2γ

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CNO Cycle

The CNO cycle features in stars larger than the sun with a higher temperature, where carbon

transmutes to nitrogen which transmutes into oxygen and ultimately returns to a carbon-12 nucleus,

resulting in the net equation producing a helium nucleus,

Hence, the carbon, nitrogen and oxygen cycle acts a catalyst.

Post-Main Sequence Stars

For older stars who have consumed most of their hydrogen, the core will begin to collapse and a layer

of heated helium will surround the core. The star’s mass will determine what proceeds. Heavier stars

will sustain the density required to fuse heavier elements (C or O) and results in a ‘helium flash’ causing

the star to become a red giant. Very massive stars keep fusing elements until iron, as all reactions are

exothermic which provide the outward radiating force preventing the star from collapsing under

gravity. However, after the formation of iron, the formation of heavier elements is unsustainable as

they require a net input of energy (endothermic). In large post-main sequence stars, the heavier

elements are drawn toward the core of the star, building up into layers with the heavier elements

toward the centre. Once the star has depleted its fuel, it succumbs to the gravitational force, causing it

to collapse, however, the increase in gravitational potential energy results in the formation of heat and

with the increase in pressure results in a large number of the outer layers to be blown outward in a

supernova. The residual core may collapse further into neutrons.

Early Experiments Examining the Nature of Cathode Rays

Cathode Rays - Waves or Particles?

Observations and Inferences Supporting Wave Theory

• Rectilinear propagation deduced from the shadows produced by the rays.

• Maltese-Cross experiment showed that a shadow was produced when a cross was placed inside the

evacuated tube.

• They passed through thin metal foils without damaging them.

Observations and Inferences Supporting Particle Theory

• Left cathode at right angles to the surface.

• Deflected by electric and magnetic fields.

• Small paddle wheels turned when placed in the path of the cathode rays, showing that cathode rays

carry and transfer momentum upon striking a paddle wheel.

• They traveled significantly slower than light.

4 11H → 4

2He + 2e+ + 2v + 3γ

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Thompson’s Plum Pudding Model

These observations then proved that the cathode rays must in fact be particulate in nature.

Observations that these rays seemed to common to all types of elements and therefore atoms

concluded that the atoms themselves had to be composed of these particles. Thompson proposed that

these discretely negatively charged sub-atomic particles, that were constituent within all atoms, were

embedded within a sea of uniform positive charge; with its mass distributed evenly but low in density,.

This sea of positive charge in his model served to effectively cancel out the negative charge of the

negative charged sub-atomic particle within an atom.

Implications of Thompson’s Charge-to-Mass Ratio Experiment

The experiment showed that cathode rays were indeed particles as Thompson was successful in

measuring a ratio, implying that the cathode rays did in fact possess a mass, and since waves

do not possess a mass, this proved that cathode rays were in fact particles. Thompson’s experiment also

showed that the electron had a large negative charge and an extremely small mass. Also, the fact that

the same charge to mass ratio was measured when different materials were used as the cathode

indicated that these particles must be common to all atoms, perpetuating the proposition that the atom

consisted of a smaller sub-atomic particle, leading to Thompson’s new model of the atom - the Plum

Pudding Model.

Millikan’s Oil Drop Experiment In 1909, Robert Millikan performed an experiment to show the quantised nature of electric charge. The

method involved tiny charged oil droplets being sprayed into a chamber with parallel electric plates

surrounding the droplets. Some of the oil droplets would have been charged due to the friction

encountered when being sprayed out of the nozzle, hence, when a voltage was applied some of the oil

droplets could be made to stop falling as the electrostatic attractive force balanced the gravitational

attraction. By equating these two forces, and after calculating the mass of the oil droplets he was able to

deduce that the charge carried by the droplets was . Millikan found that for other oil droplets

to stop falling, the voltage had to be stepped up by the same difference, as these oil droplets had picked

up different charges when being sprayed out. The minimum charge he found was , 6%

lower than the current accepted value. Any other oil droplets he found had integer multiples of this

fundamental charge, where . This resulted in the realisation that charge was quantised,

and that electrons carried the unit of electric charge.

qm

=E

rB2

q =mgd

V

1.59 × 10−19

q = Nqe N ∈ ℤ+

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Geiger-Marsden Experiment Rutherford suggested that if Thompson’s model were to be true, when alpha particles were fired at a

thin foil of gold, the alpha particles should either go straight through or experience minimal

deflections, as according to Thompson’s model if the atom were to be covered in a sea of positive

charge, it must have a low density. Hence, to test this out, Rutherford assigned his assistants Geiger and

Marsden to perform the experiment. Most of the results achieved were expected with most of the

alpha particles travelling in a straight line with minimal deflections, however 1 in 8000 of them seemed

to be deflected back at an angle greater than ninety degrees. This was revolutionary as it suggested there

was a dense positively charged mass within the atom causing a rebound.

Rutherford’s Model of the Atom From the analysis, he concluded that Thompson’s model had to be modified. He suggested that for the

alpha particles to be deflected at such angles, virtually all of the atom’s mass had to be concentrated to

a small and dense region which was positively charged - later named the nucleus. The electrons were

proposed to surround the nucleus in a circular manner. The rest, and most, of the atom had to be

empty space - which explained the predominant straight path of the alpha particles. If the alpha

particles skimmed past the nucleus or collided with the electrons, their paths would be deflected

slightly. If the alpha particles were to collide with the nucleus, they would be rebounded back at an

angle greater than ninety degrees - since the nucleus was minuscule, the chances of this happening

would be remote.

Chadwick’s Discovery of the Nucleus In 1930, German scientist Walther Bothe noted that when alpha particles bombarded beryllium, a

neutral but highly penetrative radiation was observed. This was discovered to be neutral as it was not

deflected by electric or magnetic fields. They were discovered to be particles by James Chadwick. His

setup involved firing alpha particles at beryllium atoms, after which the emitted, proposed, neutrons.

These neutrons would collide with the proton rich paraffin wax, causing it to be ejected and measured

by a detector resulting it the assessment of velocity and energy, after which, using the laws of

conservation of energy and momentum, the mass of the neutron could be calculated. Hence, the

existence of the neutron as a neutral particle was experimentally shown, and later found to be close to

the mass of a proton.

42He + 9

4Be → 126 C + 1

0n

Year 12 2019 of XXI XXIV Modules 6,7,8


Limitations of the Bohr and Rutherford Model of the Atom

Limitations of Rutherford’s Model of the Atom

• Rutherford could not explain the contents of the nucleus, although he knew it was a concentrated

mass of positive charge.

• Although he proposed the electrons to be placed around the nucleus, he could not find a definitive

arrangement.

• He could not explain how the electrons stayed in orbit without spiralling into the nucleus. As

electrons in his arrangement would undergo centripetal acceleration, an accelerating charge would

give off electromagnetic radiation, a form of energy, which would result in the loss of their kinetic

energy, causing them to spiral into the nucleus.

Limitations of Bohr’s Model of the Atom

• While Bohr could predict the largest stable radius and spectral lines of hydrogen, he could not

predict the spectral lines for any multi-electron elements, not even a simple element such as helium.

• His model could not explain the different intensities of spectral lines and why certain electron

transitions are favoured.

• His model could not explain why some of the lines split into multiple closely spaced lines - fine and

hyperfine structure - or the magnetically induced Zeeman effect.

Experimental Evidence for De Broglie’s Matter Waves In 1927, Davisson and Germer set up an experiment in which they fired electrons at a nickel crystal and

observed their behaviour as the scattered off the nickel surface. The electrons were accelerated using a

potential difference of 54 V to achieve a high velocity and directed toward the nickel crystal. Upon

striking the plane of the nickel crystal, some of the electrons would pass through gaps between the

nickel atoms which served as small enough slits so that diffraction would occur. Consequently,

interference patterns would be formed by returning electrons, and when a detector was placed, a series

of maxima and minima of electron intensity could be detected if diffraction was occurring. From the

interference pattern, they were able to measure the wavelength of the electron waves, which agreed

with de Broglie’s equation, .

Schrödinger’s Contribution to Quantum Mechanics Schrödinger applied mathematical relationships to determine the probability of finding an electron in a

Bohr atom. The solution to Schrödinger’s equation, when applied to electrons, can give the probability

of finding an electron within a particular position inside an atom. This gave rise to the idea of an

electron cloud or orbital around the nucleus, with different orbitals having different cloud shapes. The

density of the electron cloud gave the probability of the electron being found at that position.

λ =h

mv

Year 12 2019 of XXII XXIV Modules 6,7,8


Schrödinger’s Cat Thought Experiment

To show the absurdity of applying quantum ideas into the macro world, Schrödinger proposed a

thought experiment in which a cat was in a closed box and. The box contained a vial of poison which

would be opened if a Geiger counter detected any radiation from a radioisotope, which had a 50%

chance of emitting radiation. The quantum mechanical interpretation of this situation would be that

the cat would be both dead and alive until the box is opened. Observing the cat would collapse the

wave function, resulting in the cat being either dead or alive but no longer both. This interpretation, is

known as the Copenhagen interpretation, where all systems can be in all states of existence until

observed.

Alpha, Beta and Gamma Decay Neutron decay,

When a particle is emitted, an antineutrino is always released.

Similarly, when a particle is emitted, a neutrino is also always released.

Properties of Alpha, Beta and Gamma Radiation

Uncontrolled and Controlled Fission Chain Reaction A fission chain reaction occurs when more than one of the neutrons emitted from the initial fission

event causes new events to occur.

10n → 1

1p + 0−1e + v̄

β− v̄

β+ v

Alpha Particles Beta Particles Gamma Rays

Composition He nucleus. Fast moving electrons

or positrons.

High frequency EM

radiation.

Charge +2 elementary charge. None.

Mass 4 u. 0.0005 u. No rest mass.

Penetrating power Few cm in air. Few m in air. Few cm of lead.

Small deflection. Large deflection. No deflection.

Typical emission speeds 0.05c − 0.07c c

Effect of or fields⃗E ⃗B

0.3c − 0.9c

elementary charge.±1

Year 12 2019 of XXIII XXIV Modules 6,7,8


Controlled Fission Chain Reactions

In a controlled reaction, one neutron is produced per fission neutron. If the average number of

neutrons produced is less than one, the reaction dies away, if greater than one it induces a runaway

reaction.

Accounting For Energy Released During Fusion During fusion, two nuclei fuse together to form a more stable nuclei. This stable nuclei then releases

the excess nuclear energy. This process can occur for elements up to iron-56

Binding Energy The total energy needed to hold the nucleus together is called binding energy. The strong nuclear force

acts strongly when the distance between nucleons is smaller. The greater this binding energy, the harder

it is to pull the nucleus apart. The mass of the nucleus is less than the mass of the sum of the

individual nucleons. The mass defect provides the binding energy which holds the nucleus together, as

shown by Einstein’s energy-mass equivalence, . E = (Δm) c2

Year 12 2019 of XXIV XXIV Modules 6,7,8

Physics...HSC Physics Course Notes Vithushan Gandhiji Electromagnetic Spectrum Maxwell’s Equations...

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