Wave-Particle Duality

Double slit experiment

Proved light has wave-like properties

Wave interference - occurs when two waves meet
Constructive interference - waves are continuous (light bands)
Destructive interference - waves are discontinuous (dark bands)

Photoelectric effect

Proved light has particle-like properties

light of high enough frequency can eject electrons from metal

↑ intensity = ↑ electrons

↑ energy/frequency = ↑ velocity of ejected electrons

De Broglie wavelength

Proved wave-particle duality in matter
(only affects very small matter

λ_{de Broglie} is inversely proportional to momentum
greater momentum = shorter wavelength

Heisenberg Uncertainty Principle

The more precisely we know the momentum of an object, the less precisely we know its position

Exists because of all the innate dual nature of all things

How to find threshold frequency

Note: KE = 0 at threshold since there is no excess energy to give electrons velocity

v = frequency (Hz = s^-1)
Φ = work function, threshold frequency (J)

h = 6.626 × 10^-34 Js

How to find maximum kinetic energy (photoelectric effect)

h = 6.626 × 10^-34 Js
v = frequency (Hz = s^-1)
Φ = work function, threshold energy (J)

How to find work function/energy

v = frequency (Hz = s^-1)

h = 6.626 x 10-34 J x s

Φ = work function, threshold energy (J)

How to find maximum number of electrons that could be ejected

How to find De Broglie wavelength

h = 6.626 x 10-23 J×s

m = mass (kg/atoms)

v = velocity (m/s)

Note: mol → atoms (1 mol/6.022 × 10²³ atoms)

Note: to find velocity, use KE formula

How to determine if quantum or classical

If λ_{de Broglie} > size = quantum

If λ_{de Broglie} < size = classical

How to find uncertainty of momentum or position

X = position (m)

P = momentum (kg*m/s)

Δp = mΔv

m = mass (kg/atoms)

Δv = uncertainty in velocity (m/s)