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EdExcel Unit P3EdExcel Unit P3

Applications of Applications of PhysicsPhysics

N Smith

St. Aidan’s

Topic 1 – Radiation in Medicine

Medical Physics“Medical Physics” is a big branch of science and refers to using physics to investigate medical issues. Some examples:

CAT scansUltrasound

Endoscopes Radiotherapy

Introduction to Radiation“Radiation” refers to any form of energy originating from a source, and usually falls into two types:

Radiation

A wave, such as light coming from the sun

A particle, such as this alpha particle coming from the

nucleus

IntensityClearly, the intensity of radiation received by an object decreases the further out the object is. This is due to two things:

1) The radiation “spreads out” in a circle

2) It is also absorbed by the medium it travels through

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IntensityIntensityDefinition: “Intensity” means the strength of

light arriving at a certain point, and can also be called “Radiation flux density”

Energy dissipation

Clearly, a wave will get weaker the further it travels. Assuming the wave comes from a point source and travels out equally in all directions we can say:

Intensity =

(in Wm-2)

Power (in W)

Area (in m2)I =

P

4πr2

An “inverse square law”

The Law of Reflection

Incident ray

Normal

Reflected ray

Angle of incidence

Angle of reflection

Mirror

Angle of incidence = Angle of reflection

Refraction

Refraction through a glass Refraction through a glass blockblock

Light slows down and bends towards the normal due to

entering a more dense medium

Light speeds up and bends away from the normal due to entering a less dense

medium

Light slows down but is not bent, due to

entering along the normal

LensesLenses use the idea of refraction:

When light enters a MORE DENSE medium it slows down…

A prism uses this idea to split light. This happens because purple light is refracted more than red light

Converging and diverging lenses

CONVERGING (Convex)

Thickest at the centre. Thicker lenses will

cause more refraction

DIVERGING (Concave)

Thinnest at the centre. Lenses that are thicker

on the outside will cause more refraction

Ray Diagrams for LensesThe rays of light are refracted INWARDS and meet at the focus, F.

The image formed is REAL – in other words, it can be seen on a screen

The rays of light are refracted OUTWARDS.

A VIRTUAL image is formed – in other words, the image doesn’t actually exist

F

F

Ray diagrams for LensesTo draw ray diagrams follow these two rules:

1) Draw a ray from the TOP of the object PARALLEL to the axis and then going through F:

2) Draw a ray from the TOP of the object going through the CENTRE of the lens (which will be undeviated)

F

This image is REAL, UPSIDE DOWN and SMALLER than the object

FF

FF

FF

FF

The Lens EquationFor the ray diagrams you have just drawn verify that the lens equation works:

1

f

1

u

1

v= +

Focal length

Object distance

Image distance (+ sign is a real

image)

The Eye

Suspensory ligaments

Optic nerve

The Eye

Retina

Pupil

Cornea

Ciliary musclesSuspensory ligaments

Optic nerve

Lens

Iris

Seeing thingsRays of light are refracted (bent) first by the cornea and then by the lens. They focus on the retina which acts like the film in a camera or the CCD in a digital camera.

The “range of vision” for an eye is around 25cm up to infinity.

Seeing things at different distances

For distant objects the ciliary muscles

relax and the suspensory ligaments pull tight making the lens pull thin – the

light doesn’t bend as much.

For close objects the ciliary muscles

contract allowing the lens to go fat, thus bending the light

more.

Using lenses to correct vision

Short Long

More about lensesCompare thin and thick lenses:

Lenses are measured in units called “dioptres”:Power in dioptres = 1

focal length in m

…where converging lenses (for long sighted people) have positive values and diverging lenses (for short sighted people) have negative values.

Notice that these glasses have got a large curvature. How would you make strong glasses but also make them thinner and with less curvature?

Using Lasers in SurgeryLasers are being increasingly used in laser eye surgery:

What are the advantages and disadvantages of this treatment compared to using glasses or contact lenses?

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Refractive Index

Willebrord Snellius, 1580-1626

The Refractive Index of a material is a measure of the factor by which the material will bend light:

Refractive indexsin i

sin r=

Snell’s Law:

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Example questionsHere’s my law again:

1) Light passes from air into crystal with a refractive index of 1.5. Calculate the angles of refraction for light incident at 20O, 30O, 40O and 50O.

2) A ray of light travels through a vacuum and is incident upon a glass block (of refractive index 1.5) at an angle of 30O. The ray then passes into water. Draw an accurate diagram to show the path of this light as it travels from the vacuum through the glass and into the water.

Refractive indexsin i

sin r=

18/04/23Finding the Critical Angle…

1) Ray gets refracted

4) Ray gets internally reflected3) Ray still gets refracted (just!)

2) Ray still gets refracted

THE CRITICAL ANGLE

Calculating the Critical Angle

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Here’s my law again:

Refractive indexsin i

sin r=

Notice that, for the critical angle, this formula becomes:

Refractive index 1

sin c=

1) What is the refractive index of a material with a critical angle of 40O?

2) What is the critical angle for water, which has a refractive index of roughly 1.3?

1.56

50.3O

18/04/23Uses of Total Internal Reflection

Optical fibres:

An optical fibre is a long, thin, _______ rod made of glass or plastic. Light is _______ reflected from one end to the other, making it possible to send ____ chunks of information

Optical fibres can be used for _________ by sending electrical signals through the cable. The main advantage of this is a reduced ______ loss and endoscopes use this principle:

Words – communications, internally, large, transparent, signal

1) Pre-natal scanning

2) Medical treatment e.g. treating kidney stones

UltrasoundHumans can hear sounds between 20 and 20,000Hz. “Ultrasound” is the region of sound above 20,000Hz – it can’t be heard by humans. There are a number of medical uses for ultrasound:

18/04/23Calculating distances with ultrasound

The echo takes 0.8 seconds to return and the speed of sound in water is 1500ms-1. How deep is the water?

t/μs25

50

75

100 125 150 175 200

Hard question! Use the ultrasound scan to determine the width of the amniotic sac and the width of the baby’s body. The speed of sound in the fluid is 1500ms-1 and in soft tissue the speed is 1560ms-

1.

Using an oscilloscope with ultrasound

Consider a block of metal with a flaw:

20ms/div

Q. If the speed of the ultrasonic wave is 3,000m/s how far away is the flaw from the detector?

Topic 2 – X-rays and ECGs

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Charge (Q)Charge (Q)

The beam of electrons through the tube was basically an electric current because current, by definition, is a flow of charge. Each electron has a negative CHARGE. Charge is measured in Coulombs (C). We can work out how much current flows in a circuit using the equation:

I

Qn

Current = no. of charged particles per s x charge

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Example questionsExample questions

1) An electron has a charge of 1.6x10-19 C. If a million of these flow through a circuit every second what is the current?

2) In a different circuit 5,000,000,000 electrons travel from a battery to a bulb per second. What is the current?

3) Another circuit has a current of 0.01A. How many electrons are passing by every second?

1.6x10-13 per s

8x10-10 per s

6.25x1016 per s

18/04/23Electron Beams in evacuated Electron Beams in evacuated tubestubes

ee

ee

25KV

Cathode Anode

e

Fluorescent screen

“Thermionic emission”

Explain the role of each of these parts:

1) The heater

2) The potential difference between the anode and cathode

3) Why a vacuum is necessary

This beam of charged particles is basically an electric current

18/04/23Calculating the speed of the Calculating the speed of the electronselectrons

ee

ee

25KV

Cathode Anode

e

Fluorescent screen

Basically, the “electrical work done” on the electrons causes them to speed up, so we can say:

Charge x voltage = ½mv2

How fast will the electrons go in the above example?

X-Rays

X-rays are part of the electromagnetic spectrum with a high frequency and therefore high

energy. They cause ionisation (which could cause cancer).

X-ray images are possible because they are absorbed by thick, dense tissue like bone but transmitted by soft tissue. X-rays are formed

through collisions with metal targets.

Using X-raysX-rays can be used to diagnose and treat some medical conditions like the tumours in this body:

In CT scanners the X-rays are used to build up an image by “photographing” each layer of

the body at a time.

In fluoroscopes the patient is placed between an x-ray device and a fluorescent

screen:

Comparing X-rays, ultrasound and CT scans

X-rays Ultrasound CT scans

Can cause cancerBad quality image

Medium quality image

Generally safe

Ionising

Non-ionisingGood quality image

Can cause cancer

Ionising

Monitoring the Heart RateThe electrical impulses from the heart can be monitored using an electrocardiogram (ECG).

T – this wave shows the repolarization of the ventricles so that the heart returns to its normal active potential, ready for the next heart beat.

P – this electrical activity is small and corresponds to the atrium pushing blood through

to the ventricle (1 and 2)

The QRS complex – this shows electrical activity that triggers the ventricles to contract (ventricles are made of thicker muscle so a bigger action potential is needed) and push the blood through the heart to the rest of the body (3).

Heart rate and PacemakersThe heart beat is normally controlled by a group of _____ on the _____ hand side of the heart called the “pacemaker”. These cells control the heart rate by producing small ______ impulses that cause the heart to _______.

If the pacemaker fails, an _______ pacemaker can be fitted.

Words – artificial, right, cells, electrical, contract

Heart rates can be measured using the equation

Frequency = 1/time period

(In Hz) (in s)

Pulse OximetryA pulse oximeter is a device used to measure the blood oxygen level and heart rate through non-invasive methods.

It works by basically sending two different _______ of light through the _____ and the ______ of each of these wavelengths is measured by a _________. The absorbance of each wavelength is then turned into a blood-oxygen level by the attached ________.

Words – photodetector, wavelengths, computer, finger, absorbance

Topic 3 – Ionising Radiation

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The structure of the atomThe structure of the atomELECTRON –

negative, mass nearly

nothing

PROTON – positive,

same mass as neutron

(“1”)

NEUTRON – neutral,

same mass as proton

(“1”)

Atoms have a neutral charge overall as they

have the same number of electrons

as protons

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The structure of the atomThe structure of the atom

Particle Relative Mass Relative Charge

Proton 1 +1

Neutron 1 0

Electron 0 -1

MASS (Nucleon) NUMBER = number of protons + number of

neutrons

SYMBOL

PROTON (Atomic) NUMBER = number of protons (obviously)

Alpha and Beta decay1) Alpha () – an atom decays into a new atom and emits an alpha particle (2 protons and 2 ______ – the nucleus of a ______ atom)

2) Beta () – an atom decays into a new atom by changing a neutron into a _______ and electron. The fast moving, high energy electron is called a _____ particle.

3) + decay – similar to beta decay, this decay is when a proton turns into a neutron and emits a positively-charged beta particle called a _______ (+)

Unstable nucleus

Unstable nucleus

New nucleus

New nucleus

Alpha particle

Beta particle

Words – positron, proton, neutrons, helium, beta

Unstable nucleus

New nucleus

Beta + particle

Changes in Mass and Proton Number

Alpha decay:

Am241

95Np

237

93α

4

2+

11

5

0

+1C

11

6B β+

90

39Sr

90

38Y β

0

-1+

Beta - decay:

Beta + decay:

“positron”

N-Z CurveAn N-Z graph plots neutron number (N) against proton number (Z). The graph looks like this:

No.

of

neu

tron

s (N

)120

100

80

60

40

20

0

Proton number (Z) 20 40 60 80 100

Beta – emitters would be this side of the line:

Beta + emitters would be this side of the line:

Alpha emitters would be up here (above 82 protons):

N-Z curvesAn N-Z graph plots mass number (Z) against proton number (N). Here’s an example showing the decay of Uranium:

Mass

nu

mb

er

Proton number

What type of decay is

represented here?

What type of decay is

represented here?

Imagine this isotope of radon suddenly underwent + decay. What would we see on this diagram?

Fr

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QuarksQuarksBasically, scientists think everything in the universe is made from 12 fundamental particles. Two of these particles are called “up quark” and “down quark”.

Protons and neutrons are made of different combinations of three up and down quarks:

Proton

u u

d

Neutron

u d

d

Some questions:

1) Quarks have charges that are multiples of 1/3. Given the composition and charge of the proton and the neutron what are the charges on the up and down quark?

2) What happens in terms of quarks during beta + and beta – decay?

Up = +2/3, down = -1/3

An up quark turns into a down quark and vice versa

IonisationRadiation is dangerous because it “ionises” atoms – in other words, it turns them into ions by giving them enough energy to “knock off” electrons:

Ionisation causes cells in living tissue to mutate, usually causing cancer.

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Types of radiation revisitedTypes of radiation revisited1) Alpha () – an atom decays into a new atom and emits an alpha particle (2 protons and 2 ______ – the nucleus of a ______ atom)

2) Beta () – an atom decays into a new atom by changing a neutron into a _______ and electron. The fast moving, high energy electron is called a _____ particle.

3) Gamma – after or decay surplus ______ is sometimes emitted. This is called gamma radiation and has a very high ______ with short wavelength. The atom is not changed.

Unstable nucleus

Unstable nucleus

Unstable nucleus

New nucleus

New nucleus

New nucleus

Alpha particle

Beta particle

Gamma radiation

Words – frequency, proton, energy, neutrons, helium, beta

SummaryProperty Alpha Beta Gamma Positron Neutron

Charge

Mass

Penetration ability

Range in air

What is it?

Ionising ability

Exposure to RadiationPeople like me work with radiation a lot so we need to wear a “dosimeter” to record our exposure to radiation:

Radiation dose is measured in units

called “sieverts” (Sv).

How we are exposed to Radiation

We can be exposed to radiation by “irradiation” or by “contamination”:

Irradiation

“Irradiation” is when radiation “hits” us from the outside, like background radiation.

Contamination

“Contamination” is when we take radioactive sources in, like the case of Alexander Litvinenko

Gamma

18/04/23Using Radioactivity in Medicine - Tracers

A tracer is a small amount of radioactive material used to detect things, e.g. a leak in a pipe:

Gamma source

Tracers can also be used in medicine to detect tumours:

The radiation from the radioactive source is picked up above the ground, enabling the leak in the pipe to be detected.

For medicinal tracers, you would probably use a beta or gamma source with a short half life – why?

PET scannersPET scanners work by basically building up a 3-D image of something in the body by detecting radioactive emissions from a tracer.

The radioactive source would need to be produced nearby. Why is this?

Radiation can also be used in palliative care to relieve the symptoms caused by tumours.

Topic 4 – Motion of Particles

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Particle AcceleratorsParticle AcceleratorsThe CERN lab in Geneva is basically a huge particle accelerator (27km circumference). Scientists from around the world work there every day to analyse pictures like the following in order to understand our world better…

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16GeV pions colliding with stationary nuclei

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Circular MotionFor any object to travel in a circle there must be a “centripetal force” acting on it:

In this case the force is gravity.

Using Magnetic FieldsRecall:

++ -2 protons, 2 neutrons,

therefore charge = +2

1 electron, therefore charge = -1

Because of this charge, they will also be deflected by magnetic fields:

+

Region of magnetic field

1) Why did they move in opposite directions?

2) Which particle had the more curved path and why?

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The CyclotronThe Cyclotron

Ernest Lawrence

(1901-1958)

I invented the Cyclotron. It basically uses electric and magnetic fields to

accelerate particles in a circle:

p The protons accelerated in this cyclotron can then be fired at a stable isotope in order to make it radioactive. It can then be used for medical purposes.

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MomentumMomentumAny object that has both mass and velocity has MOMENTUM. Momentum (symbol “p”) is simply given by the formula:

Momentum = Mass x Velocity (in kgm/s) (in kg) (in m/s)

P

VM

What is the momentum of the following?

1) A 1kg football travelling at 10m/s

2) A 1000kg Ford Capri travelling at 30m/s

3) A 20g pen being thrown across the room at 5m/s

4) A 70kg bungi-jumper falling at 40m/s

10kgm/s

30,000kgm/s

0.1kgm/s

2800kgm/s

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Conservation of MomentumConservation of MomentumIn any collision or explosion momentum is conserved (provided that there are no external forces have an effect). Example question:

Two cars are racing around the M25. Car A collides with the back of car B and the cars stick together. What speed do they move at after the collision?

Mass = 1000kg

Mass = 800kg

Speed = 50m/s Speed = 20m/s

Momentum before = momentum after…

…so 1000 x 50 + 800 x 20 = 1800 x V…

…V = 36.7m/s

Mass = 1800kg

Speed = ??m/s

18/04/23Momentum in different Momentum in different directionsdirections

What happens if the bodies are moving in opposite directions?

Speed = 50m/s

Mass = 1000kg

Speed = 20m/s

Mass = 800kg

Momentum is a VECTOR quantity, so the momentum of the second car is negative…

Total momentum = 1000 x 50 – 800 x 20 = 34000 kgm/s

Speed after collision = 34000 kgm/s / 1800 = 18.9m/s

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Another exampleAnother exampleConsider the nuclear decay of Americium-241:

Am24195

α42

If the new neptunium atom moves away at a speed of 5x105 m/s what was the speed of the alpha particle?

Np23793

2.96x107 m/s

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More questions…More questions…1. A car of mass 1000kg heading up the M1 at 50m/s

collides with a stationary truck of mass 8000kg and sticks to it. What velocity does the wreckage move forward at?

2. A defender running away from a goalkeeper at 5m/s is hit in the back of his head by the goal kick. The ball stops dead and the player’s speed increases to 5.5m/s. If the ball had a mass of 500g and the player had a mass of 70kg how fast was the ball moving?

3. A white snooker ball moving at 5m/s strikes a red ball and pots it. Both balls have a mass of 1kg. If the white ball continued in the same direction at 2m/s what was the velocity of the red ball?

4. A gun has a recoil speed of 2m/s when firing. If the gun has a mass of 2kg and the bullet has a mass of 10g what speed does the bullet come out at?

5.6m/s

70m/s

400m/s

3m/s

18/04/23Recap question on Recap question on momentummomentum

1. Matt and Dan are racing against each other over 400m at Sports Day. Matt is running at 8m/s and catches up with Dan who is running at 6m/s. After the collision Matt stops and Dan moves slightly faster. If Matt’s mass is 60kg and Dan’s is 70kg calculate how fast Dan moves after the collision.

2. Bobbie is driving her 5kg toy car around. It is travelling at 10m/s when it hits the back of Heather’s (stationary) leg and sticks to it. Assuming Heather’s leg can move freely and has a mass of 10kg calculate how fast it will move after the collision.

12.9m/s

3.3m/s

Energy loss in collisions

We’ve also said that in a collision momentum is conserved (unless an external force acts). The same cannot usually be said for kinetic energy…For example, consider the following collision. How much kinetic energy is lost?

Kinetic energy = ½ x mass x velocity squared

in J in kg in ms-1

In previous work we looked at how to calculate an object’s kinetic energy:

Mass = 1000kg

Mass = 800kg

Speed = 50ms-1 Speed = 20ms-1

Before

Mass = 1000kg

Mass = 800kgSpeed = 20ms-1 Speed = 30ms-1

After

Energy loss in collisionsConsider a head-on collision where the cars stick together. How much kinetic energy is lost in this example? Where does all the energy go?

In this example more kinetic energy was lost. We say it was a “less elastic collision”. An “elastic collision” is one where the kinetic energy is conserved.

Speed = 10ms-1

Before

After

Speed = 50ms-1 Speed = 30ms-1

m=800Kg m=3000Kg

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Energy-mass equivalenceEnergy-mass equivalence

Einstein (1879-1955)

Energy has a mass (and vice versa). We can calculate how much energy a given mass is worth using my famous formula:

E=mc2

1) Josh has a mass of 85kg. How much energy is this?

2) A 0.5kg bowl of water is heated and gains about 10KJ of energy. How much “mass” has it gained?

18/04/23Electron-Positron Electron-Positron AnnihilationAnnihilation

Einstein (1879-1955)

We can also apply my equation to situations where electrons and positrons annihilate each other

Example question:

An electron and positron collide with each other and annihilate to produce a gamma ray. What happens to charge and mass during this process?

Charge – the positron has a charge of +1, the electron has a charge of -1 and the gamma ray has no charge so charge is conserved.

Mass – If the electron and the positron both have a mass of 9.11x10-31kg how much energy is released?

Topic 5 – Kinetic Theory and Gases

Particle theory revisionParticle theory is all about explaining the properties of solids, liquids and gases by looking at what the particles do.

In a solid the particles ______ around a _____ position. There is a ______ force of attraction between each particle and they are very _____ together

SOLIDS

Words – strong, close, vibrate, fixed

LIQUIDS

GASES

In a liquid the particles are _____ together but can move in any direction. They won’t keep a _____ shape like _____ do.

In a gas the particles are very far apart and move _____ in all directions. They often ______ with each other and because they are far apart they can be easily _______.

Words – fixed, collide, quickly, close, squashed, solids

Particle Motion in GasesGas pressure is caused by particles hitting the side of a container. Anything we do that increases those collisions will increase the pressure:

Particle Motion in GasesConsider increasing the temperature:

The particles should collide with the sides of the container _____ often, therefore the pressure is ________. This could cause the container to ______.

Pressure and Temperature in gases

P

T

Pressure and Temperature in gases

P

T

“Zero-pressure temperature”

-2730C

Absolute Temperature

Lord Kelvin, 1824-1907

“Absolute Temperature” starts at 0K and represents the temperature at which particles have zero kinetic energy. It goes up in the same

steps as OC. For example:

1) The freezing point of water is 273K2) The boiling point of water is 373K3) Room temperature is around 293K

Kinetic Energy and Temperature in gases

KE

T (in K)

Volume and Temperature in Gases

V

T0K

Jacques Charles, 1746-1823

For a constant mass of gas at fixed pressure, the volume

occupied by the gas is proportional to its absolute

temperature.

Volume and Temperature in Gases

Jacques Charles, 1746-1823

Provided the pressure of a gas stays the same we can use this

relationship to calculate the volume of a gas:

V1 = V2T1

T2

1) A gas changes in temperature from 200K to 300K. If its original volume was 2m3 what is the new volume?

2) Another gas is halved in volume. What will happen to its temperature?

3) A third gas is kept at constant pressure while being compressed from 20 litres to 15 litres. If its new temperature is 275K what was its original temperature?

3m3

It will halve

367K

Pressure and Volume in gases

Pressure Volume Pressure x volume

Particle Motion in GasesConsider decreasing the volume:

The particles should collide with the sides of the container _____ often, therefore the pressure is ________.

Pressure and Volume in gases

Conclusion

When we multiplied the pressure of a gas by its volume we found that the answer was always __ _______.

In other words, if you DECREASE the volume you _______ the pressure and so on.

“One goes up, the other goes down”

Boyle’s Law

Let’s draw this…P

1/V

P

V

Higher temperature?Robert Boyle 1627-1691

“For a fixed mass of gas at constant temperature (“isothermal”), the product of the pressure and volume is constant.”

Pressure and Volume in gases

This can be expressed using the equation:

Initial Pressure x Initial Volume = Final Press. x Final Vol.

PIVI = PFVF1) A gas has a volume of 3m3 at a pressure of 20N/m2.

What will the pressure be if the volume is reduced to 1.5m3?

2) A gas increases in volume from 10m3 to 50m3. If the initial pressure was 10,000N/m2 what is the new pressure?

3) A gas decreases in pressure from 100,000 Pascals to 50,000 Pascals. The final volume was 3m3. What was the initial volume?

4) The pressure of a gas changes from 100N/m2 to 20N/m2. What is the ratio for volume change?

40N/m2

20KN/m2

1.5m3

1:5

The Gas EquationA while ago we said that Pressure x Volume = Constant (Boyle’s Law)…

…also, we just said pressure is proportional to temperature (Pressure law)…

…and we said volume is proportional to temperature (Charles’ Law)…

Combining these three equations gives:

Pressure x volume = constant

temperature

P1V1 = P2V2

T1 T2

Some example questions

1) An ideal gas has a volume of 2m3 and a pressure of 101KPa (101,000 N/m2) at a temperature of 300K. The gas is then increased in temperature to 400K but kept at constant volume. Calculate the new pressure.

2) The same gas is then allowed to cool to 200K while being kept at constant pressure. Calculate the new volume.

3) Another gas at 300K and 101KPa is allowed to halve in volume while being kept at the same pressure. What is the new temperature?

135KPa

1m3

150K

Using this in Medicine

These principles are used in medicine in bottled gas canisters. The gas is kept at a higher pressure than atmospheric pressure.