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Chapter 01 · Part VI · Modern Physics
Revised on ____________________
Chapter 01 · Dual Nature of Radiation and Matter

A particle count that a wave theory cannot explain

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Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

The photon

ENERGY IN LUMPS, NOT IN A TRICKLE
I.Energy  E = h ν = h cλ
II.In electron-volts  E(eV) = 1240λ(nm) learn this and stop converting
III.Momentum  p = hλ = Ec rest mass zero
IV.Photons per second  N = P λh c
V.Intensity  I = N h ν brightness is a photon count
VI.Radiation pressure  absorber Ic , mirror 2Ic
VII.Speed  c in every frame
VIII.Effective mass  m = h νc² not a rest mass
II

The photoelectric effect

FOUR LAWS, ALL WAVE-PROOF
I.Einstein's equation  Kmax = h ν − φ
II.Threshold  ν0 = φh , λ0 = h cφ
III.Stopping potential  e Vs = Kmax
IV.So  Vs = he ν − φe slope h/e, intercept −φ/e
V.Law 1  no emission below ν0, however bright
VI.Law 2  Kmax depends on ν, never on intensity
VII.Law 3  the current ∝ intensity more photons, more electrons
VIII.Law 4  emission is instantaneous < 10−9 s — no time to accumulate
The four graphs
Shape
What it fixes
Photocurrent vs V, intensity varied
saturation rises, Vs fixed
intensity ⇒ current
Photocurrent vs V, frequency varied
saturation fixed, Vs moves
frequency ⇒ Kmax
Vs against ν
a straight line, slope h/e
h, and φ from the intercept
Current against intensity
straight, through the origin
one photon, one electron
A wave theory predicts a delay while energy accumulates, an intensity-dependent Kmax, and no threshold at all. All three predictions fail. The photon survives every one of them.
III

Matter waves

THE SAME h, THE OTHER WAY ROUND
I.de Broglie  λ = hp = hm v
II.From kinetic energy  λ = h√(2 m K)
III.Accelerated through V  λ = h√(2 m e V)
IV.For an electron  λ = 12.27√V Å V in volts
V.Thermal particle  λ = h√(3 m kB T)
VI.Davisson–Germer  d sin θ = n λ electrons diffract from a crystal
VII.Bohr orbit  2π r = n λ a standing matter wave
VIII.Heavy objects  λ is unmeasurably small which is why you never notice
Through 100 V
λ
Comparable with
Electron
1.23 Å
an atom — so crystals diffract it
Proton
2.9×10−3 Å
a nucleus
A 60 kg walker at 1 m s−1
1.1×10−36 m
nothing at all
IV

The numbers

NOTHING HERE SHOULD BE LOOKED UP
I.Work function  the least energy to free an electron a property of the metal surface
II.Photocell  current saturates when every electron is collected
III.Stopping potential  independent of intensity raise the brightness and Vs does not move
IV.Two metals  the Vs–ν lines are parallel same slope h/e, different intercepts
Planck
h = 6.63×10−34 J s
Photon shortcut
hc = 1240 eV nm
Electron-volt
1.6×10−19 J
Electron mass
9.1×10−31 kg
Visible photon
≈ 2 – 3 eV
Caesium, φ
2.14 eV
Zinc, φ
4.3 eV
1 Å
10−10 m
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Expecting a brighter source to give faster electrons. Intensity sets the current; frequency sets Kmax.
2Using λ = h/mv with a relativistic speed, or with the total energy in place of the kinetic energy.
3Mixing electron-volts with joules mid-calculation. Work in eV and nm, with hc = 1240 eV nm.
4Forgetting that below the threshold frequency nothing is emitted at all — no intensity can rescue it.