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A/L Physics Resources

Ultimate Formula Cheat Sheet 🧮

All complex formulas, units, and descriptions in one place. Use search below to recall equations before exams.

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Formulas Count: 47

FORMULA #01Mechanics

Final Velocity in Linear Motion

Finding the final velocity of an object moving with uniform acceleration after time t.

v=u+at\displaystyle v = u + at
vFinal Velocity (ms⁻¹)uInitial Velocity (ms⁻¹)aAcceleration (ms⁻²)tTime (s)
SI Unitms−1m s^{-1}
INTERACTIVE EXAMPLEMechanics

Final Velocity in Linear Motion

🚗 Scenario: A car starts from rest (u = 0) and accelerates at 2 ms⁻² for 5 seconds.

0m5m10m15m20m25m
🚗
Initial u: 0 ms⁻¹
Accel a: 2 ms⁻²
Time t: 0.0 s
Distance s: 0.0 m
Result Velocity v:v = 0 + (2 × 0.0) = 0.0 ms⁻¹
FORMULA #02Mechanics

Displacement in Linear Motion

Finding the displacement of an object moving with uniform acceleration during time t.

s=ut+12at2\displaystyle s = ut + \frac{1}{2}at^2
sDisplacement / Distance (m)uInitial Velocity (ms⁻¹)tTime (s)aAcceleration (ms⁻²)
SI Unitmm
INTERACTIVE EXAMPLEMechanics

Displacement in Linear Motion

🚗 Scenario: A car starts with 5 ms⁻¹ (u = 5) and accelerates at 2 ms⁻² for 4 seconds.

0m10m20m30m36m
🚗
Initial u: 5 ms⁻¹
Accel a: 2 ms⁻²
Time t: 0.0 s
Result s:s = (5×0.0) + (0.5×2×0.0²) = 0.0 m
FORMULA #03Mechanics

Velocity-Displacement Equation

Calculating final velocity or displacement when time is not known.

v2=u2+2as\displaystyle v^2 = u^2 + 2as
vFinal Velocity (ms⁻¹)uInitial Velocity (ms⁻¹)aAcceleration (ms⁻²)sDisplacement / Distance (m)
SI Unit(ms−1)2(m s^{-1})^2
INTERACTIVE EXAMPLEMechanics

Velocity-Displacement Equation

Variable Breakdown

Calculating final velocity or displacement when time is not known.

Formula variables:

v2=u2+2asv^2 = u^2 + 2as
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FORMULA #04Mechanics

Newton's Second Law

The net force acting on an object is equal to the product of its mass and acceleration.

F=ma\displaystyle F = ma
FForce (N)mMass (kg)aAcceleration (ms⁻²)
SI UnitNN
INTERACTIVE EXAMPLEMechanics

Newton's Second Law

📦 Scenario: A 5 kg block (m = 5) is pushed with an acceleration of 4 ms⁻² (a = 4).

StartEnd
➔📦
Mass m: 5 kg
Accel a: 4 ms⁻²
Required Force F:F = 5 × 4 = 20 N
FORMULA #05Mechanics

Momentum

The product of the mass and velocity of a moving object.

p=mv\displaystyle p = mv
pMomentum (kg m s⁻¹)mMass (kg)vFinal Velocity (ms⁻¹)
SI Unitkgms−1kg m s^{-1}
INTERACTIVE EXAMPLEMechanics

Momentum

Variable Breakdown

The product of the mass and velocity of a moving object.

Formula variables:

p=mvp = mv
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FORMULA #06Mechanics

Mechanical Work

Work done when a force displaces an object at an angle to the direction of the force.

W=Fscos⁡θ\displaystyle W = Fs \cos \theta
WWork Done (J)FForce (N)sDisplacement / Distance (m)θAngle θ (degrees/radians)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Mechanical Work

Variable Breakdown

Work done when a force displaces an object at an angle to the direction of the force.

Formula variables:

W=Fscos⁡θW = Fs \cos \theta
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FORMULA #07Mechanics

Kinetic Energy

The dynamic energy possessed by an object of mass m moving with velocity v.

Ek=12mv2\displaystyle E_k = \frac{1}{2}mv^2
EₖKinetic Energy (J)mMass (kg)vFinal Velocity (ms⁻¹)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Kinetic Energy

Variable Breakdown

The dynamic energy possessed by an object of mass m moving with velocity v.

Formula variables:

Ek=12mv2E_k = \frac{1}{2}mv^2
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FORMULA #08Mechanics

Gravitational Potential Energy

The energy possessed by an object placed at a height h in a gravitational field.

Ep=mgh\displaystyle E_p = mgh
EₚPotential Energy (J)mMass (kg)gGravitational Acceleration (~9.81 ms⁻²)hHeight / Depth (m)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Gravitational Potential Energy

Variable Breakdown

The energy possessed by an object placed at a height h in a gravitational field.

Formula variables:

Ep=mghE_p = mgh
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FORMULA #09Mechanics

Power

The rate of doing work or the rate at which energy is consumed.

P=Wt or P=Fv\displaystyle P = \frac{W}{t} \text{ or } P = Fv
PPower (W) or Pressure (Pa)WWork Done (J)tTime (s)FForce (N)vFinal Velocity (ms⁻¹)
SI UnitWW
INTERACTIVE EXAMPLEMechanics

Power

Variable Breakdown

The rate of doing work or the rate at which energy is consumed.

Formula variables:

P=Wt or P=FvP = \frac{W}{t} \text{ or } P = Fv
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FORMULA #10Matter

Density

The mass contained in a unit volume of a substance.

ρ=mV\displaystyle \rho = \frac{m}{V}
ρDensity (kg m⁻³)mMass (kg)VVolume (m³) or Voltage (V)
SI Unitkgm−3kg m^{-3}
INTERACTIVE EXAMPLEMatter

Density

Variable Breakdown

The mass contained in a unit volume of a substance.

Formula variables:

ρ=mV\rho = \frac{m}{V}
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FORMULA #11Matter

Pressure

The force acting perpendicularly on a unit area of a surface.

P=FA\displaystyle P = \frac{F}{A}
PPower (W) or Pressure (Pa)FForce (N)AArea (m²)
SI UnitPaPa
INTERACTIVE EXAMPLEMatter

Pressure

Variable Breakdown

The force acting perpendicularly on a unit area of a surface.

Formula variables:

P=FAP = \frac{F}{A}
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FORMULA #12Mechanics

Hydrostatic Pressure

The pressure exerted by a liquid column at depth h in a liquid of density ρ.

P=hρg\displaystyle P = h\rho g
PPower (W) or Pressure (Pa)hHeight / Depth (m)ρDensity (kg m⁻³)gGravitational Acceleration (~9.81 ms⁻²)
SI UnitPaPa
INTERACTIVE EXAMPLEMechanics

Hydrostatic Pressure

Variable Breakdown

The pressure exerted by a liquid column at depth h in a liquid of density ρ.

Formula variables:

P=hρgP = h\rho g
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FORMULA #13Matter

Upthrust

The upward net force exerted by a fluid on an object immersed in it.

U=Vρg\displaystyle U = V\rho g
UInitial Velocity (ms⁻¹)VVolume (m³) or Voltage (V)ρDensity (kg m⁻³)gGravitational Acceleration (~9.81 ms⁻²)
SI UnitNN
INTERACTIVE EXAMPLEMatter

Upthrust

Variable Breakdown

The upward net force exerted by a fluid on an object immersed in it.

Formula variables:

U=VρgU = V\rho g
Interactive Card
FORMULA #14Mechanics

Hooke's Law

Within the limit of elasticity, the extension produced in a wire or spring is directly proportional to the applied force.

F=kx\displaystyle F = kx
FForce (N)kSpring Constant (N m⁻¹)xExtension (m)
SI UnitNN
INTERACTIVE EXAMPLEMechanics

Hooke's Law

Variable Breakdown

Within the limit of elasticity, the extension produced in a wire or spring is directly proportional to the applied force.

Formula variables:

F=kxF = kx
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FORMULA #15Mechanics

Young's Modulus

A measure of the elasticity of a solid material (tensile stress / tensile strain).

Y=FlAe\displaystyle Y = \frac{Fl}{Ae}
yYoung's Modulus (N m⁻²)FForce (N)lLength (m)AArea (m²)eExtension (m) or Emissivity
SI UnitNm−2N m^{-2}
INTERACTIVE EXAMPLEMechanics

Young's Modulus

Variable Breakdown

A measure of the elasticity of a solid material (tensile stress / tensile strain).

Formula variables:

Y=FlAeY = \frac{Fl}{Ae}
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FORMULA #16Thermal

Heat Capacity & Temperature Change

The amount of heat required to be supplied to or removed from an object of mass m to change its temperature.

Q=mcΔθ\displaystyle Q = mc\Delta\theta
QHeat Energy (J) or Charge (C)mMass (kg)cSpecific Heat Capacity (J kg⁻¹ K⁻¹)
SI UnitJJ
INTERACTIVE EXAMPLEThermal

Heat Capacity & Temperature Change

Variable Breakdown

The amount of heat required to be supplied to or removed from an object of mass m to change its temperature.

Formula variables:

Q=mcΔθQ = mc\Delta\theta
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FORMULA #17Thermal

Latent Heat

The heat required to change the physical state of an object without changing its temperature.

Q=ml\displaystyle Q = ml
QHeat Energy (J) or Charge (C)mMass (kg)lLength (m)
SI UnitJJ
INTERACTIVE EXAMPLEThermal

Latent Heat

Variable Breakdown

The heat required to change the physical state of an object without changing its temperature.

Formula variables:

Q=mlQ = ml
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FORMULA #18Thermal

Ideal Gas Law

The relationship between pressure, volume, number of moles, and absolute temperature of an ideal gas.

PV=nRT\displaystyle PV = nRT
PPower (W) or Pressure (Pa)VVolume (m³) or Voltage (V)nMoles of GasRUniversal Gas Constant (8.314 J mol⁻¹ K⁻¹)TAbsolute Temperature (K)
SI Unit−-
INTERACTIVE EXAMPLEThermal

Ideal Gas Law

Variable Breakdown

The relationship between pressure, volume, number of moles, and absolute temperature of an ideal gas.

Formula variables:

PV=nRTPV = nRT
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FORMULA #19Waves

Wave Speed

The relationship between the speed of any wave, its frequency, and its wavelength.

v=fλ\displaystyle v = f\lambda
vFinal Velocity (ms⁻¹)fFrequency (Hz)λWavelength (m)
SI Unitms−1m s^{-1}
INTERACTIVE EXAMPLEWaves

Wave Speed

🌊 Scenario: A wave oscillates at a frequency of 10 Hz with a wavelength of 0.5 m.

Frequency f: 10 Hz
Wavelength λ: 0.5 m
Wave Speed v:v = 10 × 0.5 = 5 ms⁻¹
FORMULA #20Waves

Period of a Simple Pendulum

The time taken by a simple pendulum of length l for one complete oscillation.

T=2πlg\displaystyle T = 2\pi\sqrt{\frac{l}{g}}
TAbsolute Temperature (K)lLength (m)gGravitational Acceleration (~9.81 ms⁻²)
SI Unitss
INTERACTIVE EXAMPLEWaves

Period of a Simple Pendulum

Variable Breakdown

The time taken by a simple pendulum of length l for one complete oscillation.

Formula variables:

T=2πlgT = 2\pi\sqrt{\frac{l}{g}}
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FORMULA #21Electricity

Ohm's Law

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

V=IR\displaystyle V = IR
VVolume (m³) or Voltage (V)ICurrent (A)RUniversal Gas Constant (8.314 J mol⁻¹ K⁻¹)
SI UnitVV
INTERACTIVE EXAMPLEElectricity

Ohm's Law

Variable Breakdown

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

Formula variables:

V=IRV = IR
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FORMULA #22Electricity

Electrical Power

The rate at which electrical energy is consumed in an electrical circuit or device.

P=VI=I2R=V2R\displaystyle P = VI = I^2 R = \frac{V^2}{R}
PPower (W) or Pressure (Pa)VVolume (m³) or Voltage (V)ICurrent (A)RUniversal Gas Constant (8.314 J mol⁻¹ K⁻¹)
SI UnitWW
INTERACTIVE EXAMPLEElectricity

Electrical Power

Variable Breakdown

The rate at which electrical energy is consumed in an electrical circuit or device.

Formula variables:

P=VI=I2R=V2RP = VI = I^2 R = \frac{V^2}{R}
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FORMULA #23Electricity

Resistors in Series

Finding the equivalent resistance when several resistors are connected in series (in line).

Rs=R1+R2+R3+...\displaystyle R_s = R_1 + R_2 + R_3 + ...
RResistance (Ω)
SI UnitΩ\Omega
INTERACTIVE EXAMPLEElectricity

Resistors in Series

Variable Breakdown

Finding the equivalent resistance when several resistors are connected in series (in line).

Formula variables:

Rs=R1+R2+R3+...R_s = R_1 + R_2 + R_3 + ...
Interactive Card
FORMULA #24Electricity

Resistors in Parallel

Finding the equivalent resistance when several resistors are connected in parallel.

1Rp=1R1+1R2+...\displaystyle \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + ...
RResistance (Ω)
SI UnitΩ\Omega
INTERACTIVE EXAMPLEElectricity

Resistors in Parallel

Variable Breakdown

Finding the equivalent resistance when several resistors are connected in parallel.

Formula variables:

1Rp=1R1+1R2+...\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + ...
Interactive Card
FORMULA #25Waves

Wien's Displacement Law

The relationship between the wavelength corresponding to maximum intensity (λ_m) emitted by a blackbody and its absolute temperature (T).

λmT=C\displaystyle \lambda_m T = C
λWavelength (m)TAbsolute Temperature (K)
SI UnitmKm K
INTERACTIVE EXAMPLEWaves

Wien's Displacement Law

Variable Breakdown

The relationship between the wavelength corresponding to maximum intensity (λ_m) emitted by a blackbody and its absolute temperature (T).

Formula variables:

λmT=C\lambda_m T = C
Interactive Card
FORMULA #26Mechanics

Stefan's Law

The total radiated power per unit area of a perfect blackbody is directly proportional to the fourth power of its absolute temperature.

E=σT4\displaystyle E = \sigma T^4
EExtension (m) or EmissivityσStefan-Boltzmann ConstantTAbsolute Temperature (K)
SI UnitWm−2W m^{-2}
INTERACTIVE EXAMPLEMechanics

Stefan's Law

Variable Breakdown

The total radiated power per unit area of a perfect blackbody is directly proportional to the fourth power of its absolute temperature.

Formula variables:

E=σT4E = \sigma T^4
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FORMULA #27Mechanics

Total Radiated Power of a Blackbody

Calculating the total thermal radiation power emitted by a perfect blackbody of surface area A.

P=AσT4\displaystyle P = A \sigma T^4
PPower (W) or Pressure (Pa)AArea (m²)σStefan-Boltzmann ConstantTAbsolute Temperature (K)
SI UnitWW
INTERACTIVE EXAMPLEMechanics

Total Radiated Power of a Blackbody

Variable Breakdown

Calculating the total thermal radiation power emitted by a perfect blackbody of surface area A.

Formula variables:

P=AσT4P = A \sigma T^4
Interactive Card
FORMULA #28Mechanics

Radiated Power of a Non-Blackbody

Calculating the total thermal radiation power emitted by a general object with emissivity (e).

P=eAσT4\displaystyle P = e A \sigma T^4
PPower (W) or Pressure (Pa)eExtension (m) or EmissivityAArea (m²)σStefan-Boltzmann ConstantTAbsolute Temperature (K)
SI UnitWW
INTERACTIVE EXAMPLEMechanics

Radiated Power of a Non-Blackbody

Variable Breakdown

Calculating the total thermal radiation power emitted by a general object with emissivity (e).

Formula variables:

P=eAσT4P = e A \sigma T^4
Interactive Card
FORMULA #29Mechanics

Energy of a Photon

The basic equation to find the energy of a single photon with frequency f or wavelength λ.

E=hf=hcλ\displaystyle E = hf = \frac{hc}{\lambda}
EExtension (m) or EmissivityfFrequency (Hz)λWavelength (m)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Energy of a Photon

Variable Breakdown

The basic equation to find the energy of a single photon with frequency f or wavelength λ.

Formula variables:

E=hf=hcλE = hf = \frac{hc}{\lambda}
Interactive Card
FORMULA #30Mechanics

Planck's Equation

The total energy of n photons of electromagnetic radiation with frequency f.

E=nhf\displaystyle E = nhf
EExtension (m) or EmissivitynMoles of GasfFrequency (Hz)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Planck's Equation

Variable Breakdown

The total energy of n photons of electromagnetic radiation with frequency f.

Formula variables:

E=nhfE = nhf
Interactive Card
FORMULA #31Mechanics

Threshold Frequency and Work Function

The relationship between the minimum energy required to liberate an electron from a metal surface (work function) and the threshold frequency.

ϕ=hf0\displaystyle \phi = hf_0
ϕWork Function (J)fFrequency (Hz)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Threshold Frequency and Work Function

Variable Breakdown

The relationship between the minimum energy required to liberate an electron from a metal surface (work function) and the threshold frequency.

Formula variables:

ϕ=hf0\phi = hf_0
Interactive Card
FORMULA #32Mechanics

Maximum Kinetic Energy and Stopping Potential

The relationship between the maximum kinetic energy of electrons emitted in the photoelectric effect and the stopping potential (V_s) required to stop them.

Kmax=eVs\displaystyle K_{max} = e V_s
KmaxMax Kinetic Energy (J)VVolume (m³) or Voltage (V)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Maximum Kinetic Energy and Stopping Potential

Variable Breakdown

The relationship between the maximum kinetic energy of electrons emitted in the photoelectric effect and the stopping potential (V_s) required to stop them.

Formula variables:

Kmax=eVsK_{max} = e V_s
Interactive Card
FORMULA #33Mechanics

Einstein's Photoelectric Equation

The conservation of energy relationship between the energy of the incident photon, the work function of the metal, and the maximum kinetic energy of the emitted electron.

hf=ϕ+Kmax\displaystyle hf = \phi + K_{max}
fFrequency (Hz)ϕWork Function (J)KmaxMax Kinetic Energy (J)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Einstein's Photoelectric Equation

Variable Breakdown

The conservation of energy relationship between the energy of the incident photon, the work function of the metal, and the maximum kinetic energy of the emitted electron.

Formula variables:

hf=ϕ+Kmaxhf = \phi + K_{max}
Interactive Card
FORMULA #34Waves

De Broglie Wavelength

The wavelength of the matter wave associated with a particle of mass m moving with velocity v.

λ=hp=hmv\displaystyle \lambda = \frac{h}{p} = \frac{h}{mv}
λWavelength (m)pMomentum (kg m s⁻¹)mMass (kg)vFinal Velocity (ms⁻¹)
SI Unitmm
INTERACTIVE EXAMPLEWaves

De Broglie Wavelength

Variable Breakdown

The wavelength of the matter wave associated with a particle of mass m moving with velocity v.

Formula variables:

λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}
Interactive Card
FORMULA #35Mechanics

De Broglie Wavelength using Kinetic Energy

Calculating the matter wavelength of a particle with kinetic energy K.

λ=h2mK\displaystyle \lambda = \frac{h}{\sqrt{2mK}}
λWavelength (m)mMass (kg)EₖKinetic Energy (J)
SI Unitmm
INTERACTIVE EXAMPLEMechanics

De Broglie Wavelength using Kinetic Energy

Variable Breakdown

Calculating the matter wavelength of a particle with kinetic energy K.

Formula variables:

λ=h2mK\lambda = \frac{h}{\sqrt{2mK}}
Interactive Card
FORMULA #36Mechanics

De Broglie Wavelength using Accelerating Potential

The De Broglie wavelength of an electron accelerated from rest through a potential difference V.

λ=h2mVe\displaystyle \lambda = \frac{h}{\sqrt{2mVe}}
λWavelength (m)mMass (kg)VVolume (m³) or Voltage (V)
SI Unitmm
INTERACTIVE EXAMPLEMechanics

De Broglie Wavelength using Accelerating Potential

Variable Breakdown

The De Broglie wavelength of an electron accelerated from rest through a potential difference V.

Formula variables:

λ=h2mVe\lambda = \frac{h}{\sqrt{2mVe}}
Interactive Card
FORMULA #37Waves

X-Ray Minimum Wavelength

The minimum wavelength of X-rays (in continuous spectrum) that can be produced by electrons accelerated through potential V.

λmin=hceV\displaystyle \lambda_{min} = \frac{hc}{eV}
λWavelength (m)VVolume (m³) or Voltage (V)
SI Unitmm
INTERACTIVE EXAMPLEWaves

X-Ray Minimum Wavelength

Variable Breakdown

The minimum wavelength of X-rays (in continuous spectrum) that can be produced by electrons accelerated through potential V.

Formula variables:

λmin=hceV\lambda_{min} = \frac{hc}{eV}
Interactive Card
FORMULA #38Mechanics

Einstein's Mass-Energy Equivalence

The total amount of energy released when the mass of matter is converted into energy.

E=mc2\displaystyle E = mc^2
EExtension (m) or EmissivitymMass (kg)cSpecific Heat Capacity (J kg⁻¹ K⁻¹)
SI UnitJJ
INTERACTIVE EXAMPLEMechanics

Einstein's Mass-Energy Equivalence

Variable Breakdown

The total amount of energy released when the mass of matter is converted into energy.

Formula variables:

E=mc2E = mc^2
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FORMULA #39Mechanics

Mass Defect

The difference between the total mass of free constituent nucleons and the actual mass (M) of the nucleus formed.

Δm=Zmp+(A−Z)mn−M\displaystyle \Delta m = Z m_p + (A-Z) m_n - M
ρDensity (kg m⁻³)mMass (kg)VVolume (m³) or Voltage (V)
SI Unitkg/ukg / u
INTERACTIVE EXAMPLEMechanics

Mass Defect

Variable Breakdown

The difference between the total mass of free constituent nucleons and the actual mass (M) of the nucleus formed.

Formula variables:

Δm=Zmp+(A−Z)mn−M\Delta m = Z m_p + (A-Z) m_n - M
Interactive Card
FORMULA #40Mechanics

Nuclear Binding Energy

The binding energy holding a nucleus together due to its mass defect. Practically calculated as 931.5 MeV per 1 u.

BE=Δm×c2\displaystyle BE = \Delta m \times c^2
EExtension (m) or EmissivitymMass (kg)
SI UnitJ(orMeV)J (or MeV)
INTERACTIVE EXAMPLEMechanics

Nuclear Binding Energy

Variable Breakdown

The binding energy holding a nucleus together due to its mass defect. Practically calculated as 931.5 MeV per 1 u.

Formula variables:

BE=Δm×c2BE = \Delta m \times c^2
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FORMULA #41Mechanics

Law of Radioactive Decay (Differential)

The rate of decay of a radioactive sample at any instant is directly proportional to the number of active nuclei present at that instant.

dNdt=−λN\displaystyle \frac{dN}{dt} = -\lambda N
NMoles of GastTime (s)λWavelength (m)
SI Units−1s^{-1}
INTERACTIVE EXAMPLEMechanics

Law of Radioactive Decay (Differential)

Variable Breakdown

The rate of decay of a radioactive sample at any instant is directly proportional to the number of active nuclei present at that instant.

Formula variables:

dNdt=−λN\frac{dN}{dt} = -\lambda N
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FORMULA #42Mechanics

Activity of a Sample

Finding the activity of a sample at any instant using the number of active nuclei (N) and the decay constant (λ).

A=λN\displaystyle A = \lambda N
PPower (W) or Pressure (Pa)λWavelength (m)NMoles of Gas
SI UnitBqBq
INTERACTIVE EXAMPLEMechanics

Activity of a Sample

Variable Breakdown

Finding the activity of a sample at any instant using the number of active nuclei (N) and the decay constant (λ).

Formula variables:

A=λNA = \lambda N
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FORMULA #43Mechanics

Radioactive Decay Equation

The number of active radioactive nuclei (N) remaining after time t in a sample that initially had N₀ nuclei.

N=N0e−λt\displaystyle N = N_0 e^{-\lambda t}
NMoles of GasλWavelength (m)tTime (s)
SI Unit−-
INTERACTIVE EXAMPLEMechanics

Radioactive Decay Equation

Variable Breakdown

The number of active radioactive nuclei (N) remaining after time t in a sample that initially had N₀ nuclei.

Formula variables:

N=N0e−λtN = N_0 e^{-\lambda t}
Interactive Card
FORMULA #44Mechanics

Activity Decay Equation

Calculating the activity (A) of a sample after time t, where the initial activity was A₀.

A=A0e−λt\displaystyle A = A_0 e^{-\lambda t}
PPower (W) or Pressure (Pa)λWavelength (m)tTime (s)
SI UnitBqBq
INTERACTIVE EXAMPLEMechanics

Activity Decay Equation

Variable Breakdown

Calculating the activity (A) of a sample after time t, where the initial activity was A₀.

Formula variables:

A=A0e−λtA = A_0 e^{-\lambda t}
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FORMULA #45Mechanics

Half-life

The time taken for exactly half of the initial radioactive nuclei in a sample to decay.

T1/2=ln⁡2λ=0.693λ\displaystyle T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}
TAbsolute Temperature (K)λWavelength (m)
SI Unitss
INTERACTIVE EXAMPLEMechanics

Half-life

Variable Breakdown

The time taken for exactly half of the initial radioactive nuclei in a sample to decay.

Formula variables:

T1/2=ln⁡2λ=0.693λT_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}
Interactive Card
FORMULA #46Mechanics

Carbon Dating Time Equation

Finding the age (t) of archaeological samples using their Carbon-14 activity level.

t=1λln⁡(A0A)\displaystyle t = \frac{1}{\lambda} \ln\left(\frac{A_0}{A}\right)
tTime (s)λWavelength (m)
SI Units/Yearss / Years
INTERACTIVE EXAMPLEMechanics

Carbon Dating Time Equation

Variable Breakdown

Finding the age (t) of archaeological samples using their Carbon-14 activity level.

Formula variables:

t=1λln⁡(A0A)t = \frac{1}{\lambda} \ln\left(\frac{A_0}{A}\right)
Interactive Card
FORMULA #47Electricity

Radius of Charged Particle in Magnetic Field

The radius of the circular path of a particle of charge q moving with velocity v inside magnetic flux density B.

r=mvqB\displaystyle r = \frac{mv}{qB}
rVariablemMass (kg)vFinal Velocity (ms⁻¹)qCharge (C)BMagnetic Field (T)
SI Unitmm
INTERACTIVE EXAMPLEElectricity

Radius of Charged Particle in Magnetic Field

Variable Breakdown

The radius of the circular path of a particle of charge q moving with velocity v inside magnetic flux density B.

Formula variables:

r=mvqBr = \frac{mv}{qB}
Interactive Card