Physics Notes.docx

Acceleration of an object towards the center of a circular track when in constant circular motion, where acceleration is perpendicular to Linear Velocity

Centripetal Force

The resultant force on a body towards the center of a circle keeps an object in constant circular motion.

Tangential/Linear Velocity

The velocity of an object is tangential to its circular motion.

Formulas
Angular Displacement Formula

Θ=s/r

Angular Velocity Formula

ω=∆Θ/∆t =2π/t(Full cycle) =v/r

Centripetal Acceleration Formula

a=ω²r =v²/r =vω
Centripetal Force Formula

F=ω²rm =v²m/r

Variables Used
s=Distance travelled around a circle ( Arc Length), Θ=Angular Displacement, t=Time, v=Tangential/Linear Velocity, r=Radius of the Circle, ω=Angular Velocity

Gravitational Fields

Definitions

Gravitational Field

A Region of space around a body in which a point mass experiences a force

Gravitational Field Strength

Force per unit mass acting on a test mass at a given point

Gravitational Potential Energy

Work done in bringing a test mass from infinity to a defined point

Gravitational Potential

Work done per unit Mass in bringing a test mass from infinity to a defined point

Newton's Law of Gravitation (Gravitational Force)

The Force between two point masses is directly proportional to the product of both their masses and inversely proportional to the Square of their separations from their centers.

Kepler’s Third Law

The square of the Time Period for an object in circular orbit around a point mass, is directly proportional to the cube of the radius of its orbit.

Geostationary Orbit

An orbit in which the time period is equal to the time period of rotation of the earth/ or given point mass.

Formulas

Newton's Law of Gravitation (Gravitational Force)

F=(G*m1*m2)/x²

Gravitational Field Strength

g=F/(m2)=G(m1)/x² ( when u substitute newton's law of gravitation)

Gravitational Potential Energy

G.P.E=mgh ( at distances closer to the surface) =-G(m1)(m2)/x

Δ G.P.E. = mΔΦ

Gravitational Potential

Φ =-G(m1)/x

Kepler’s Third Law

T²=(4π²/G(m1))*r³

Variables/Constants Used

F=force, G=Newton’s Gravitational Constant, m1=Mass of Point mass( in orbital questions, this is the mass being orbited), m2=Mass of second point mass, T= Times Period for 1 Orbit, x=separation from their centres, r= Radius of Orbit, m=mass, g=Gravitational Field Strength, h=change in height Φ = gravitational potential.

Need to know

How to Draw a Gravitational Field Around a Point Mass

For Point Mass:Field Lines should look like they originate from the centre, and are moving towards it ( gravitational fields are always attractive)
Uniform: Parallel lines that are equi-distant to each other, towards the ground/mass.

Relate Centripetal Force and Gravitational Force (During Orbit) To Derive:

Kepler’s Formula (T² α r³)

Gravitational Force Gives Necessary Centripetal Force
ω²r(m2)=G(m1)(m2)/r²
ω²=G(m1)/r³
ω=2π/T ∴ω²=4π²/T²
4π²/T²=G(m1)/r³
4π²r³/T²=G(m1)
T²=4π²r³/G(m1)

Tangential Velocity In Orbit

Gravitational Force Gives Necessary Centripetal Force
v²(m2)/r=G(m1)(m2)²
v²=G(m1)/r
v=sqrt(G(m1)/r)

What Happens to the Change in Gravitational Potential Energy?

it gets converted to other forms like Kinetic energy or heat, if it says no energy is lost, the relation ∆KE=∆GPE can be used to find Kinetic Energy or Velocity at a given point after Change in Position.

0.5(m2)v²=G(m1)(m2)/x²,
v²=2G(m1)/x²,
v=sqrt(2G(m1)/x²)

Gravitational Field Strength against Separation Graph

Around 1 point mass

g=G(m1)/r²
gα1/r²
so it should be a Curve, going downwards (opening up), starting at r=1, with max gravitational Strength, and should divide by 4 consecutively for each integer increase of r.

Between 2 point Masses

it would be a decreasing curve from max at the radius of the first point mass, that would go through the x axis at 1 point, and emerge on the other axis, this is due to the Gravitational Field switching directions, it would then decrease till a max field strength when the point is on the surface of the 2nd point mass.

Why is the sign for GPE negative?
As an object moves away from earth, its gravitational Potential energy increases as it does work on itself, to move to infinity, at infinity GPE ∝ 1/∞², 1/∞²=0, ∴at infinity GPE is 0 but a maximum, therefore for any values of x where 0<x<∞, it should be below 0, that is why the negative sign is vital

Other Commonly Asked Questions/Points to Remember

Compare between Uniform point mass and non-uniform point mass

Similarities:

Both are Attractive
Both are Radial

Differences:

Not uniform at surface

Why are Fields approximately Uniform at the surface in Point Masses?

As you get closer to the surface, the field lines tend to be more parallel in nature, as uniform fields have parallel lines which attribute to its uniform nature, the Point mass tends to have a more uniform nature of gravitational field.

How are planets considered to be point masses?

Planets are considered to be point mass’s when the distance of separation is much much larger compared to the radius/length of the sphere.

Why is there a point between two large pointmasses, where gravitational field strength is zero?

As you get closer to a point mass, its field strength increases, and as you get away it decreases, at 1 point between two point masses, the field strength acting on an object from each point mass equalises, but due to the nature of both being opposite in direction, they cancel each other out.

Describe a Geostationary Orbit.

Equatorial orbit from west to east with a time period that is equal to that of Earth's.

Temperature

Definitions

Thermal Energy

the energy possessed by an object due to its temperature

Thermal Equilibrium

When objects, in physical contact, with each other no longer exchange thermal energy due to both reaching the same temperature.

Absolute Zero

The lowest Temperature Possible, where atoms and molecules have zero kinetic and potential Energy.

Specific Heat Capacity

The amount of thermal energy required to raise a unit mass of a substance by 1 degree kelvin..

Specific Latent Heat

The Amount of Thermal Energy required to change the state of a unit mass of a substance at constant temperature.

Formulas

Heat Capacity

°K=°C+273

Heat Capacity

Q=mc∆T

Latent Heat of Fusion

Q=mLf

Latent Heat of Vaporisation

Q=mLv

Variables used

°K=Degree Kelvin, °C=Degree Celsius, Q=Thermal Energy, m=Mass of substance, c=Specific Heat of a substance, Lf=latent heat of fusion, Lv=Latent Heat of vaporisation, ∆T= change in temperature.

Need to know

Direction of Thermal Energy Flow

Thermal Energy Always flows from the region with most energy to the region with least energy, until both Regions are equal in Energy.

Why is Specific Latent Heat of Vaporisation Larger than Specific Latent Heat of Fusion?

When Substances convert from liquid to gas, the particles are separated to infinity, and the particles need to do work against the atmosphere, as such, it requires more energy.

Ideal Gas

Definitions

Avagadros Constant

number of molecules in 1 mole of a substance

Ideal Gas

a gas that follows the relationship PvαT at all thermodynamic temperatures, pressures and volumes.

Mole

amount of a substance

Formulas

Avogadro's constant

Na=N/n

Boltzmann constant

K=R/Na

Ideal Gas

Pv=nRT

Pv=NKT

Pv=(Nm<C>²)/3

Gas Formulas
P1V1=P2V2 (Temperature is constant)

T1/P1=T2/P2 (Volume is constant)

T1/V1=T1/V2 (Pressure is constant

Need to know

Assumptions of Ideal Gas

Volume of a gas particle is negligible compared to the total volume of the whole gas.
Force between gas particles is negligible, as they are separated by an infinite distance.
Gas particles collide elastically with each other.
Gas Particles are always in motion
Time of a collision is negligible compared to the time between collisions

How to Derive Square Speed Equation

https://www.savemyexams.co.uk/a-level/physics/cie/22/revision-notes/15-ideal-gases/15-2-kinetic-theory/15-2-2-derivation-of-the-kinetic-theory-of-gases-equation/

(if u ran out of “free revision notes”, just use a new incognito window)

How to Find kinetic Energy

Pv=(Nm<C>²)/3 Pv=NKT
NKT=(Nm<C>²)/3
3NKT=Nm<c>²
3KT=m<c>²
Ek=(mv²)/2=(m<c>²)/2
∴Ek=(3KT)/2

Thermodynamics

Definitions

Internal Energy

The sum of the random distribution of potential and kinetic energies of its molecule

First law of Thermodynamics/Conservation of energy

It states that energy can neither be created nor destroyed but only altered from 1 form to another.

Formulas

First Law of Thermodynamics

∆u=q+w

Work done by a gas

w=p∆v

Variables used

∆u is internal energy, q is thermal energy added into the system, w is the work being done on the gas, p is pressure and ∆v is Change in Volume

Need to know

Ways in which internal energy can be

Determined

Temperature of the substance
the motion of the molecules
State of Matter

Changed

Increased by adding heat and doing work on it
Decreased by losing heat to the surroundings

Relation of Internal Energy and Temperature in gases

Internal energy comprises potential energy and kinetic energy but in ideal gases, potential energy is zero but a maximum due to gas molecules being separated by an infinite distance, so majority/all the kinetic energy is the internal energy.Temperature is the average kinetic energy of a substance, as such when temperature increases the particles gain more kinetic energy, so internal energy is directly proportional to temperature.

Work done in Constant Pressure and Volumes

When pressure is constant, and volume changes, there is a magnitude of work done by/on the gas but there is no work done when pressure increases while volume is constant

Simple Harmonic Motion

Definitions

Simple Harmonic Motion

In Periodic Motion, if the acceleration is directly proportional to its displacement but in the opposite direction it is in Simple Harmonic Motion

Oscillation

The back and forth motion of an object on either side of any equilibrium Position.

Amplitude

The maximum displacement of an oscillator from its equilibrium position

Displacement

The distance of an oscillator from its equilibrium Position

Time period

The time taken for 1 oscillation in seconds

Hooke's Law

Force is directly proportional to its extension in the same direction

Spring Constant

Force Per Unit Extension, Measure of the stiffness of a spring. Springs with large spring constants have high stiffness

Restoring Force

A force that acts to bring back the object to equilibrium

Phase Difference

tells us how much behind or ahead a wave is relative to another wave

Path Difference

The difference in distance travelled by two waves from their sources to the point where they meet.

Elastic Potential Energy

the energy stored in a spring when stretched due to the work done in stretching it

Free Oscillations

An Oscillation where periodic Forces are not applied, therefore undergoing Damping if resistive forces are present

Forced Oscillations

An Oscillation where periodic forces are applied to sustain the oscillation

Damping

When the total energy and amplitude of the oscillations decreases while having constant frequency and time period due to resistive forces acting on the oscillator

Natural Frequency

The Frequency of an oscillation in free Oscillations

Driving Frequency

The frequency of forced oscillations

Resonance

When the driving frequency of an oscillation is equal to the natural frequency of an oscillation, the resulting amplitude and total energy of the oscillations increases significantly.

Formulas

Hooke’s Law

F=Kx

Acceleration in simple Harmonic Motion

a=-ω²x

Acceleration (Mass spring system)

a=(-kx)/m

Acceleration (Simple Pendulum)

a=(-gx)/l

Max Velocity ( Mass Spring System)

Vmax=√(k/m)*X0

Need To Know

Acceleration Derivation

Spring Mass System

restoring force is upwards for a spring stretched down but opposite to its displacement ∴ F=-kx
using newton's 2nd law, F=ma
ma=-kx
a=-kx/m

Pendulum System

Angular Displacement is Θ=s/r, in this case it's Θ=x/l
at low values of Θ ( between 0-20°), Sin(Θ)=Θ, ∴sin(Θ)=x/l
Restoring Force=-mgsin(Θ)
F=-mgx/l
F=ma ( Newton’s Second Law)
ma=-mgx/l
a=-gx/l

Energy of An Oscillator

Simple pendulum

At Equilibrium At Rest

Has Gravitational Potential Energy Only but a minimum ( so we count it as base energy (0))

At Amplitude points

Has Gravitational Potential Energy Only But a Maximum as work is done on the system to move it to the amplitude point

At Points Between Equilibrium and Amplitude

Has gravitational Potential Energy and Kinetic Energy, Where sum of Energies is Equal to the energies at Amplitude Points

At Equilibrium After Quarter Oscillation

Max Kinetic energy as all the lost GPE is converted to Kinetic Energy

Mass Spring System

At Equilibrium At Rest

Has 0 Energy ( G.P.E and Internal Energy can be ignored)

At Amplitude points

Has Maximum Elastic Potential Energy

At Points Between Equilibrium and Amplitude

Has Elastic Potential Energy and Kinetic Energy, with sum adding up to Maximum Elastic Potential Energy

At Equilibrium After Quarter Oscillation

Has Maximum Kinetic Energy as all the lost EPE is converted to Kinetic Energy

Graphical Representation

Displacement

similar to a Cosine Graph

Velocity

Similar to a Negative Sine Graph

Acceleration

Similar to a Negative Cosine Graph

Kinetic Energy

Graphs with max at Quarter and 3 quarter mark with zeros at start, mid and End.

GPE/EPE

Graph with max at start and mid and End with zeros at quarter and 3 quarter marks of time period.

Derivation of Max Velocity

at Equilibrium Kinetic Energy is Max, Kinetic energy is directly proportional to Velocity, so velocity is max at equilibrium.
∴E.Kmax=E.P.Emax
E.P.Emax=0.5kX0²
E.Kmax=0.5mVmax²
0.5mVmax²=0.5kX0²
Vmax²=kX0²/m
Vmax=√(k/m)*X0
ω=√(k/m)
Vmax=ω*X0

Derivation of Velocity at a Point Between

Total Energy=KE+EPE
Total Energy=KEmax
KEmax=KE+EPE
0.5mVmax²=0.5mv²+0.5kx²/m
v²=Vmax²-(kx²/m)
v²=(ωx0)²- (kx²/m)
v²=ω²x0²-ω²x²
v²=ω²(x0²-x²)
v=±ω√(x0²-x²)

Resonance Graph with damping

when the driving frequency= the natural frequency of the oscillator, it undergoes resonance, where the amplitude and energy increases significantly. the peak decreases as damping increases.

Damping Types:

Light Damping

a type of damping in which the energy and displacement is lost gradually with every oscillation

Heavy Damping

a type of damping where the energy and displacement is lost gradually but with no oscillation

Critical damping

a type of damping where the energy and displacement is lost in the shortest time possible.

Electric Fields

Definitions

Electric Field

Electric field is a region of space where a positive test charge experiences a force due to the presence of an electric field

Electric Field Strength

Force per unit positive charge acting on a Stationary Charge

Electric Potential Energy

Work Done in bringing a positive test charge from infinity to a defined point

Electric Potential

Work Done per unit charge in bringing a positive test charge from infinity to a defined point.

Coulomb's Law (ElectroStatic Force)

Electrostatic Force between two point charges is directly proportional to the product of both their charges, but inverse to the square of their separation .

Formulas

Coulomb’s Law ( ElectroStatic Force)

F=(q1)(q2)/4π(ε0)x²

Electric Field Strength

Around a Point Charge:E=F/(q2)=(q1)/4π(ε0)x²

in a Uniform Field:E=-V/d

Electric Potential

Around a Point Charge:V=(q1)/4π(ε0)x

in a Uniform Field:V=-E*d

Electric Potential Energy

Around a Point Charge:V=(q1)(q2)/4π(ε0)x

in a Uniform Field:E=V*q=E*d*(q2)

Variables/Constants Used

E=Electric Field Strength, (q1)=Point Charge 1, (q2)=Point Charge 2, F=Force, d=distance, (ε0)=Permittivity of Free Space, x= Separation of charged from Surface

Need to Know

Field Lines:

Direction of Field Lines

Always Away From Positive Charge and Toward Negative Charge

Field Lines in a Uniform Field

Equidistant to each other, Parallel, and in a direction away from Positive Plate and Towards Negative Plate.

Field Lines Around a Point Charge

Radial Around a Point Charge, Moving away if its Positive Charge and Moving towards if negative Charge. The Radial Lines Should look like they originate from the Centre of the Charge.

Field Lines Around 2 point Charges

Two Like Positive Charges

All Lines Should have an arrow showing Field is Away from the charges, empty space in between the Charges, with bent deviated Lines around this space, with no intersection lines.

Two like Negative Charges

All Lines should have an arrow showing the field is toward the charges, empty space in between the charges, with bent deviated lines around this space, with no intersecting lines.v

Unlike Charges

Field Lines move away from Positive Charge, and towards Negative Charge, lines moving from the middle of both charges, should be closer but parallel together in the middle of the charges, with distance increasing as you move from the middle.

Field Strength Against distance Graph:

Around a Point Charge

The Field Strength Decreases by 1/4th for Every integer increase of separation

2 Positive Charges fig(ii)

Field Strength would decrease from max from the surface of the sphere till a point where it is 0, then decrease more as it gets closer to the other charge. In the end, the Electric field strength would be negative as the field changes direction.

2 Negative Charges fig(iv)

The Field Strength would increase till a point where it is 0, then increase as it closer to the other charge. In the end, the electric field strength would be positive as the field would change direction.

Unlike Charges

Field Strength would never change direction so in both cases, + to - or - to +, it would be on the same quadrant. if + to - it would be in the 1st quadrant fig(i), if - to + it would be in the 4th quadrant fig(iii)

Other Common Asked Questions/Points to Remember

Why is Electric Potential constant inside a Charged Sphere?

Capacitance

Definitions

Capacitance

Charge Per Unit Potential Difference where charge is built on 1 plate, and potential difference across both plates.

Time Constant

The time taken for the no. of Charge to decrease to 37% of its initial Charge

Formulas

Capacitance
C=Q/V

Charge

Q=CV

Voltage

V=Q/C

Energy Stored in Capacitor

E=QV/2=CV²/2=Q²/2C

Energy Supplied to capacitor

E=QV=CV²=Q²/C

Total Capacitance in Parallel

CTotal=C1+C2+...

Total Capacitance in Series

Ctotal=1/(1/C1+1/C2+…)

Discharge of a Capacitor

X = Xo*e^(–t/RC)

Time Constant

t=RC

Variables Used

C=Capacitance, Q=Charge, V=Potential Difference, E=Energy, t=time, e=exponential constant, R=Resistance.

Need to Know

Graphs

During Charging

Current

When the Capacitor is charging, the build of charge creates an electric field that repels new charges, causing the rate of charge added into the plate to decrease. so it would be a decreasing Curve, but with decreasing magnitude .

Charge

When the Capacitor is charging, due to the repulsive effect induced by charges already on the plate, the rate of charge entering decreases. so the graph would be a curve with an increasing curve, but with decreasing magnitude of Gradient.

Potential Difference

When the Capacitor is charging,. as Q=CV, QαV so Potential Difference graph would be an increasing curve, but with decreasing magnitude of Gradient ( same as charge).

During Discharge

Current

At the start of the discharging process, current is max as charge Leaving the capacitor is high, due to the huge repulsive effect from built up Charge, and current decreases with decreasing gradient as charge loss decreases as time, which decreases the repulsive effect. so a Decreasing curve is made

Charge

At the start of the discharging process, Charge is max as charge is built on the plate, Charge decreases as time goes, with a max gradient at the start, due to the repulsive effect. but gradient decreases

Potential Difference

Q=CV, QαV so potential difference would be a decreasing curve, but with decreasing magnitude of Gradient ( would be same as charge)

Energy Stored

When you draw a Graph of V against Q, the Gradient is 1/capacitance, the Energy stored can be found by finding the area under the graph, the graph should be a line passing through the origin and increasing linear graph.

Charge Discharge Graph Time Constant Graph

Similar to a Radioactive Decay Graph, at t=time constant, the charge in the should be 0.37

Dielectric Insulator

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Magnetic Fields

Definitions

Magnetic Field

A Region of Space where FerroMagnetic and Magnetic Materials Experience a Force Created by moving Charge Particles, Current Carrying Conductors, or Permanent magnets

Magnetic Flux Density

Force Acting Per Unit Length Per Unit Current that is Experienced by a Current Carrying Conductor Placed in a Magnetic field at 90 degree Angles

Tesla

Uniform Max Flux Density when a Current Carrying Conductor Of 1 meter at 90 degree angles in a magnetic Field Experiences a Force of 1 Newton while Carrying a Current of 1 Ampere

Hall Voltage

potential difference measures across a current carrying Plate due to the build of up charges on one side of the plate

Formulas

Force on a straight conductor

F=BILsin(Θ)

Force on a moving charge

F=BqvSin(Θ)

Hall voltage Formula

V=BI/(ntq)

Need to Know

Direction of Magnetic Field

Magnetic Fields are always from North Pole to south pole

MaxWell’s Right Hand Rule

For a Current Carrying Conductor, the Magnetic Field created can be found using MaxWells Right Hand Rule, where the thumb shows direction of Current, and The Other Fingers show direction of field.

Current Carrying Conductor in a magnetic field (Motor Effect)

A Current Carrying Conductor would create its own magnetic field, when placed in another Magnetic Field, the interaction between both magnetic Fields would create a force, this is known as the motor effect

Fleming’s Left Hand Rule

Used to find the Force Experienced at a point by a charge, or a current carrying conductor due to it being in a Magnetic Field at 90 Degree angles. The Index would be the direction of the magnetic Field, the Middle finger would be the direction of current and the thumb would be the direction of Force experienced.

Current Balance Experiment

A Current is connected to a circuit, is kept in the field of a U shaped Magnetic Field, that is set on a Weight Balance so inturn a current Balance Experiment is set up like this:(picture on the right)

How to find Magnetic Flux Density

When current flows through the wire, it experiences a force, using fleming's left hand rule, we can see the force is downwards, due to this force an equal force in the opposite direction is applied on the magnet(Newton’s Third Law), which is upwards, this causes the Balance to have a change in value, the force can be calculated using this difference of new and old value (F=∆m*a). if we draw a graph of Force against change in Current, F=(BL)*I, BL=g, B=g/L.

Direction of Force of a Moving Charge in a Magnetic Field

When we use Fleming's left hand rule, we can find the direction of the force, where the motion of the charge is taken into account instead of current.

Motion of a Charge Particle Moving in a uniform magnetic Field, Perpendicular to the direction of Motion

The charged Particle would move in a Circular Motion, as the magnetic field would provide the necessary Centripetal Force for it as its perpendicular to the motion of the particle.

Magnetic Field and Electric Field as a Velocity Selector

When an electric field is added in such a way that the force exhibited by the electric field is opposite to the magnetic force on the charge, a velocity selector can be set up when both forces are equalised.

Field Lines in Long Straight Wire

Circular Magnetic field, which u can obtain the direction of Magnetic field Lines, using Maxwell's right hand thumb rule.

Field Lines in a Long Solenoid

Magnetic Field Lines would be uniform inside the solenoid and circular outside, with the Lines towards the exit of the current (North Pole of the Solenoid).

FIeld Lines in a Helmholtz Coils

Similar to the field lines in a solenoid

What does adding a Ferrous Core to a solenoid do?

it concentrates the fields together as such the strength of the magnetic field increases.

Force Between current Carrying Conductors

if the direction of current is in the same direction in both wires, the forces are towards each other, if not,they are in opposite directions.

How to derive Hall Voltage?

when the hall probe works on the principle of a electric field being built up due to electrons gathering on one side of the plate as such we can use the equation E=Vh/d, and F=qe to form the equation F=(qVh)/d which can be equated to F=Bqv
Bqv=qVh/d

Vh=Bvd
we use the equation I=Anvq
rearrange and substitute in the equation to replace v
Vh=(BId)/(Anq)
A=d*t
Vh=(BId)/(dtnq)
Vh=(BI)/(tnq)

ElectroMagnetic Induction

Definitions

ElectroMagnetic Induction

the process in which e.m.f is induced in a closed circuit due to change in magnetic flux

Magnetic Flux

it is the product of magnetic flux density and the cross sectional area perpendicular to the direction of magnetic flux density

Magnetic Flux Linkage

Product of magnetic flux and no.of turns in a coil

Faraday’s Law

the amount of emf induced into a coil is directionally proportional to the rate of change of Magnetic flux linkage

Lenz’s Law

the direction of emf induced into a coil, is in such a way that it opposes the change that caused it

Formulas

Magnetic Flux

Φ=BA

Magnetic Flux Linkage

magnetic flux linkage=BAN

Faraday’s Law

E.M.F=-N∆Φ/∆t

Need to Know

Alternating Current

Definitions

Peak Current

Max Current in an Alternating Current

Peak Voltage

MaxVoltage in an Alternating Current

Period

Time taken for one complete cycle of an Alternating Current

Frequency

Amount of Cycles of Alternating current per unit time

Rectification

The process of converting Alternating current to Direct current.

Smoothing

the process of smoothing rectified waves to have a stable constant direct current

Root mean Square Value

it is the value of direct current which would give rise to the same heating effect in an resistor in alternative current

Formulas

Representing Sinusoidal A.C

x=x0sin(ωt)

Mean Power

Root Mean Square

Need to Know

Quantum Physics

Definitions

Photons

discrete packets of energy in Electromagnetic Radiation

PhotoElectric Effect

Phenomenon where electrons are emitted from the surface of a metal, after the absorption of electromagnetic energy

Threshold Frequency

The Minimum Frequency of electromagnetic energy required for a metal to emit a photoelectron from its surface

Threshold Wavelength

The Maximum Wavelength of electromagnetic energy required for a metal to emit a photoelectron from its surface

Work Function

The minimum Energy to release a photoelectron from the surface of a metal

Intensity

it is the measure of the no. of incident photons on a metal

PhotoElectric Current

Photoelectric current is the measure of photoelectrons emitted per second from the surface of a metal.

Electron Diffraction

bending of electron particles around atomic structures such as a Graphite slit, to produce a diffraction pattern on a screen

DeBroglie’s Wavelength

The Wavelength Associated with a moving particle

Excitation

Absorption of energy in electrons allows it to move from 1 energy state to a higher energy state

Formulas

Photon Energy

E=hf

Photon Momentum

p=e/c=hc/λc p=h/λ

eV to J

1ev=1.6*(10^-19)J

PhotoElectric Equation

E= Φ+ 0.5mv²max

De broglie’s Equation

λ=(h/p)=(h/mv)

Discrete Energy Change

hf=(E1)-(E2)
(hc)/(λ)=(E1)-(E2)

λ=(hc)/(E1)-(E2)

Need to know

What does the photoelectric Effect show?

It provides evidence that light can be quantised/ in discrete packets, as an electron absorbs light in a 1:1 ratio, this means that frequency above the threshold frequency will emit electrons.
PhotoElectric Graph Representation

E= Φ+ 0.5mv²max, E.Kmax=0.5mv²max and E=hf
hf=Φ+ E.Kmax
Rearrange the equation to make y=mx+c
E.Kmax=hf-Φ
Draw graph of Max Kinetic energy against frequency

the gradient would be planck's constant, the Y intercept would be a work function, and it should be below the x axis.

Intensity and Photoelectric Current

Intensity is directly proportional to photoelectric current as intensity increases the no. of photons incident on the metal by which it increases the no. of photoelectrons emitted.

Electron K.E against Intensity

The Kinetic Energy of the Emitted Electron is not influenced by Intensity, as electrons take in photons in a 1:1 ratio, so even if the amount of photons absorbed per second is high, the electrons absorb the same photon energy, which means that the kinetic energy is constant and not effected. this can also be shown by the Equation E.Kmax=hf-Φ

Electron Diffraction Experiment

When a Beam of Electrons are accelerated through a thin film of Graphite, the electrons diffract and produce a circular pattern on a fluorescent screen

Observations:

AS Voltage increases, the diameters of the rings decrease

Atomic Energy Levels

Specific Energies that electrons in an atom can have

Ground State

it is the lowest energy level that electrons occupy in ground atoms

Excited State

Any Energy Level above its ground state that an electron occupies, is said to be an electron in its excited state.

Ionised State

the state that an electron becomes when it gains enough energy to leave the atom

LINE SPECTRUM NEXT PAGE

Line Spectrums

Lines Spectrums are used to find patterns for each element, used to compare the patterns of unknown patterns to find the Elemental composition of unknown objects or materials.

Emission Spectra

When an electron moves from a higher energy level to a lower energy level, it results in the emission of a photon, each transition corresponds to a different wavelength and to a line in a spectrum of series lines against a black background

Absorption Spectra

When an electron moves from a lower energy level to a higher energy level, it results in the absorption of a photon, each transition corresponds to a different wavelength and to an empty dark line in a continuous spectrum.

Nuclear Physics

Definitions

Binding Energy

The amount of energy needed to break apart a nucleus into separate nucleons to infinity.

Mass defect

The difference in mass of a nucleon and the mass of its protons and neutrons when separated to infinity.

B.E Per Nucleon

The average energy needed to remove a nucleon

Nuclear Fusion

When two light nuclei with lower Binding Energy Per Nucleon combine to form 1 larger heavy nuclei with higher Binding energy Per Nucleon

Nuclear Fission

When a heavy nuclei breaks down to two lighter nuclei with similar mass, due to the bombardment of a Particle.

Radioactive Decay

the disintegration of an unstable energy rich nuclei to form a more stable nuclei, by the emission of Alpha, Beta or Gamma Particles.

Decay Constant

The Probability that a nucleus will decay per unit time

Activity

No. of Decays per unit time

Half Life

The amount of time taken for a mass of a nuclear sample to decay to half of its original mass.

Formulas

Atomic Notation

A
X
Z

Mass Defect

∆m=(Z*mp+(A-Z)*mn)-matom

Binding Energy

E = (Δm)c²

Binding Energy Per Nucleon

Eb per Nucleon=Eb/A

Activity

A=-(∆N/∆T)=λN

Radioactive Decay Equation

N=N0e^(–λt)
A=A0e^(–λt)

Half life

T½ =0.693/λ

Need to Know

Why is there a Mass Defect?

When a nucleus is formed, it requires energy known as binding energy, this additional energy is obtained by converting some of its mass to energy.

B.E per Nucleon Graph Against Nucleon Number

Binding energy per Nucleon graph is drawn like this:

Significance of a B.E/nucleon Graph

Peaks at nucleon no. 56±4 as they are the most stable

below 56, most tend to undergo Nuclear Fusion, and above most tend to undergo Nuclear Fission.

Difference between fission and radioactive decay

Radioactive decay is natural, while Nuclear fission requires Bombardment of a particle to start. Radioactive decay gives products that are similar to the original Nuclei, while Nuclear fission splits the nuclei to give products with the same mass.

Characteristics of a Radioactive Decay

Random

Radioactivity can not be predicted as they decay at different times independent of each other.

Spontaneous

Radioactivity cannot be affected by external environmental conditions as the nucleus isn't affected by such conditions

Why is the count Rate from a Geiger Meter not Equal to Activity(A)?

Some Radiations do not reach the counter of geiger meter due to

Some get absorbed by the surrounding materials between the counter and the radioactive materials like air or any shielding.
Radiations travel in all directions, so some might not go close to the counter, leading to a defective rate.
Background Radiation is present in the count rate.
Daughter Nuclei might be Radioactive

Why are there spikes in the count rate graph of a Nuclear Sample?

Probability of decay is same for all nuclei independent of each other so any nucleus can decay or not decay whenever they want

Why is there a negative sign on the Activity Equation?

Activity decreases as time goes on, as activity is directly proportional to the amount of nucleons remaining in the original sample, so it is negative

Radioactive Decay Graph ( A/t or N/t)

Radioactive decay graph is shown by the equations

N = N0e^(–λt)
A = A0e^(–λt)
When we draw the graphs of both of these, it is a negative decay graph.

Calculating Decay Constant

N=N0*e^(-λt)
at t=t½
½N0=N0*e^(-λt½)
ln(½)=ln(e)*-λt½
0.693=λt½
λ=0.693/t½

Medical Physics

Astronomy and Cosmology

Definitions

Luminosity

Total Power Radiated by a star

Radiant Flux Intensity

The observed amount of energy per unit radiated normally through a surface area

Standard Candles

An Astronomical Object which has a known luminosity due to a characteristic quality possessed by the class of the object.

Cepheid Variables

A Star in which the Radius and Temperature Changes Periodically which hence changes the luminosity periodically.

Surface Temperature

Temperature at the surface of an Astronomical Object, most notably stars

Wien's Displacement Law

The Peak Wavelength of a Black Body Radiation Intensity curve is Inversely Proportional to its Surface Temperature.

Stefan-Boltzmann’s Law

the total energy emitted by a blackbody per unit area per second is directly proportional to the fourth power of the absolute temperature of the body.

Hubble’s Law

The Drift speed of galaxies away from earth is directly proportional to their distance from the earth.

RedShift

The apparent shift in Wavelength of spectras when compared to known patterns, towards the red side of the color spectrum, of distant stars, due to them moving further from us

Formulas

Inverse Square Law of Flux

F=L/4πd²

Wien's Displacement Law

λmaxT=2.9*10^-3

Stefan Boltzmann’s Law

L=4πr²σT^4

Red Shift Formula

∆λ/λ =∆f/f =v/c

Hubble’s Law

V=H0d

Need to Know

What are the Assumptions made for the Inverse Square law of Flux?

Power of the star radiates uniformly through space
No Radiation is absorbed while transmitting

How to Use Standard Candles

Direct Distance measurement can be done if the object is close to earth, but for far indirect methods are involved.

Standard Candles are used as the distance can be estimated based on how bright it appears on earth.
Standard Candles can be used to measure distances within a certain distance

What's a Black Body?

it is a theoretical object, which

Absorbs all radiation fallen on it, and good at emitting
it doesn't reflect or transmit any radiation

Wien’s Law Derivations

Shorter the wavelength ( closer to the blue spectrum), the star tends to be hotter

How to use Stefan Boltzmann’s Law?

We use Wien's Law, Stefan Boltzmann’s law and inverse flux intensity (if luminosity is not given), we use Wien’s displacement law to find the surface temperature, we find Luminosity using inverse flux intensity, and then we input it in the formula to find radius of a given star.

Derivations from Hubble’s Law?

Further the galaxy is from earth, the faster its recession speed
The gradient of a graph of recession velocity against distance is hubble’s constant

Emission Spectra

the spectra pattern of an element does not change, so when you observe light from a distant source, they have the same pattern but has “Red Shifted”, these spectras can be compared with the spectras of the element with the same pattern, and the speed of recession can be found using Doppler redshift equations.

Expanding Universe

Doppler Redshift shots that all galaxies are receding
The more red shifted a Galaxy is, the Faster the galaxy is moving away

Big Bang Theory

All Parts of the universe are moving away from each other, with more distant objects moving faster. This shows that in the past all matter must have come from a dense point in the universe.

Age of the Universe

We Relate time with Hubble’s Constant using substitution
V=d/t
d/t=H0d
t=1/H0
We Sub Hubble’s Constant and find age, this is why Hubble's constant is sought after a lot by astronomers.

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