PHY 132 T4 Formulas

Lorentz factor

where

γ = Lorentz factor

v = relative speed

c = speed of light (3×10^8m/s)

Time Dilation

where

Δt = dilated time

Δt0​ = proper time.

γ = Lorentz factor

Length Contraction

where

γ = Lorentz factor

L0 = proper length

L = contracted Length

Lorentz Transformations

where

γ = Lorentz factor

x-hat = position in a moving frame

x = position in one frame

t= time

v = speed frame

t-hat = time in a moving frame

c = speed of light (3×10^8m/s)

Relativistic velocity addition

where

u = velocity in one frame

u’ = velocity in moving frame

v= frame speed

c= speed of light (3 × 10^8m/s)

Relativistic Momentum

where

p = relativistic momentum

γ = Lorentz factor

m0 = rest mass

v = speed

Relativistic Kinetic Energy

where

γ = Lorentz factor

K = Kinetic Energy

m0 = rest mass

c = speed of light (3×10^8m/s)

Total Energy

where

γ = Lorentz factor

E = total Energy

m0 = rest mass

c = speed of light (3 × 10^8m/s)

Rest Energy

Where

E0 = Rest energy

γ = Lorentz factor

m0 = rest mass

c = speed of light (3 × 10^8m/s)

Planck and Photon Energy

where

E = Photon Energy

h = Planck’s Constant (6.626 × 10^-34 J x s)

f = frequency

c = speed of light (3 × 10^8 m/s)

lambda = wavelength

Photon Momentum

where

p = photon momentum

E = photon energy

c = speed of light (3 × 10^8m/s)

h = Planck’s Constant (6.626 × 10^-34 J x s)

f = frequency

lambda = wavelength

Photoelectric effect

where Kmax​ = max electron kinetic energy,

ϕ = work function,

f = frequency.

h = Planck’s Constant (6.626 × 10^-34 J x s)

Threshold Frequency

where

f0 = threshold frequency

ϕ = work function

h = Planck’s Constant (6.626 × 10^-34 J x s)

Number of photons

Where

N = number of photons

Etotal = Total Energy

h = Planck’s Constant (6.626 × 10^-34 J x s)

f = frequency

Photons per Second

where

N/t = photons per second

P = power

h = Planck’s Constant (6.626 × 10^-34 J x s)

f = frequency

Compton Effect

where

λ′ = scattered wavelength,

λ = initial wavelength,

θ = scattering angle.

h = Planck’s Constant (6.626 × 10^-34 J x s)

me = electron mass (9.11 × 10^-31 kg)

c = speed of light ( 3 × 10^8 m/s)

de Brogile Wavelength (Relativistic)

where

lambda = de Broglie wavelength

h = Planck’s Constant (6.626 × 10^-34 J x s)

p = photon momentum

de Brogile Wavelength (non-relativistic)

where

lambda = de Brogile wavelength

m = mass

v = speed

Hydrogen Spectral Lines

where

λ = emitted wavelength,

R = Rydberg constant(1.097 × 107 m−1)

nf​ = final level,

ni​ = initial level.

Angular Momentum Quantization

where

me = electron mass (9.11 × 10^-31 kg)

v = orbital speed,

rn​ = orbit radius,

n = principal quantum number.

Allowed orbit radii for Hydrogen

where

rn​ = orbit radius,

n = quantum number,

aB​ = Bohr radius (.529 × 10^-10m)

Hydrogen Energy Levels

where

En​ = energy of level n,

n = principal quantum number.

Ionization energy

For hydrogen from ground state: 13.6 eV.

Where (from level n):

• E ionize from n = Ionization energy for n state

• En = Energy level n

• n = principal quantum number

Transition Energy and Emitted Photon

where

ΔE = transition energy,

Ei​ = initial energy,

Ef​ = final energy,

f = frequency,

λ = wavelength.

h = Planck’s Constant (6.626 × 10^-34 J x s)

c = speed of light (3 × 10^8m/s)

Orbit Radius (Hydrogen-like ion)

where

rn,Z​ = orbit radius for hydrogen-like ion,

Z = nuclear charge number.

n = principal quantum number

aB​ = Bohr radius (.529 × 10^-10m)

Energy Levels (Hydrogen-Like ions)

where

En,Z​ = energy level for hydrogen-like ion,

Z = nuclear charge number.

n = principal quantum number

Total Energy (relativistic momentum)

Where

E = total energy

p = relativistic momentum

c = speed of light (3 × 10^8 m/s)

m0 = rest mass

Bohr’s radius

where

aB = bohr’s radius

me​ = electron mass (9.11 × 10^-31 kg)

k = Coulomb constant (9 × 10^9 Nm²/C²)

e = charge magnitude (1.6 × 10^-19 C)

de Brogile frequency

where

f = frequency

h = Planck’s constant (6.626 × 10^-34 J x s)

E = total energy

Element Notation

where

Z = atomic number

A = number of nucleons

X = chemical symbol for element

N = number of neutrons

Radioactive Decay

where

N(t) = number of nuclei at time t

N0 = initial number of nuclei (i.e. at t = 0)

lambda = “decay constant” (related to t1/2 by lambda = ln2/t1/2)

Relativistic mass

where

m(v) = relativistic mass

γ = Lorentz factor

v = velocity

c = speed of light (3×10^8m/s)

Mass defect

where

delta m = mass defect

Z = number of protons

mp = proton mass (1.00728amu)

N = number of neutrons

mn = neutron mass (1.00867 amu)

1 amu = 1.66054 × 10^-27kg “=“ 931.5MeV

Mnucleus = nucleus mass

Binding energy per Nucleon

Where

BE/A = Binding energy per nucleon

A = Number of nucleons (Mass number)