🌳 Concept tree

├── Why electrons stay inside a metal

• ├── Thermionic emission and the cathode-ray tube (CRT)

├── The photoelectric effect

├── Einstein's explanation (1905)

├── Stopping potential and the graphs

├── Using the energy unit eV

├── Worked examples (Lesson 2)

├── The Compton effect

├── Properties of the photon

├── Radiation force (light pressure)

├── Macroscopic and microscopic models of light

├── Reflection or transmission of photons

├── Worked examples (Lesson 3)

├── De Broglie's idea (1923)

• ├── Why do we not notice the wave nature of a ball?

├── Wavelength of an accelerated electron

├── The electron microscope

├── Worked examples (Lesson 4)

├── Chapter summary (key points)

└── Common mistakes to avoid

• Einstein adopted Planck’s idea and applied it to light itself: light travels as photons, each photon carrying energy E = hν.
• The explanation is:

• One photon gives all of its energy to one electron, in a single instantaneous event (this explains the absence of delay).

• • A certain minimum energy is needed to free an electron from the metal surface.
  • This minimum energy is called the work function, E_w (also written Φ or W).
  • It depends on the type of metal only.
  • Electrons deeper in the metal or more tightly bound need more energy.

• The threshold frequency is the frequency whose photon energy exactly equals the work function:

  E_w = h ν_c (5-1) and the threshold wavelength λ_c = c/ν_c = hc/E_w.

• If hν < Ew the electron is not released, whatever the intensity (many weak photons cannot combine their energies because each electron interacts with one photon).
• If hν = Ew the photon just frees the electron, with zero kinetic energy.
• If hν > Ew the electron is freed and the extra energy appears as its kinetic energy.

• Einstein’s photoelectric equation:
• hν = Ew + KEmax , that is, ½ m v²_max = h ν − h ν_c (5-2)
• Here KEmax is the maximum kinetic energy electrons emitted from the surface layer need only Ew; electrons coming from deeper layers lose some energy on the way, so they emerge with less.
• What the equation tells us:

• KE_max depends on the frequency ν (and on the metal through ν_c). It does not depend on the intensity.
• Doubling the intensity doubles the number of photons per second, so it doubles the number of photoelectrons per second (the current), but each electron still has the same maximum kinetic energy.
• The threshold frequency depends on the material only; it does not depend on the intensity of the light, the time of exposure, or the potential difference between cathode and anode.
• Einstein received the 1921 Nobel Prize in Physics for this explanation.

• When X-rays or gamma rays (high-energy photons) fall on a free electron (or a loosely bound one):

• the frequency of the scattered radiation is lower than that of the incident radiation (the photon has lost energy), and its direction changes;
• the electron recoils its speed increases from rest and it moves off in another direction.

• The wave theory cannot explain this, because a wave would simply make the electron vibrate and re-radiate at the same frequency.
• The effect is explained easily if light is treated as particles.
• The photon collides with the electron like one billiard ball hitting another, and two conservation laws apply:

• For these laws to be usable, the photon must have momentum just as the electron has.
• The Compton effect therefore proves that a photon is a particle that has energy and momentum.

• Whether a beam is reflected or passes through a medium depends on comparing λ with the distance between the atoms of the medium.
• If λ is much larger than the spacing, the photons "see" a continuous surface and are reflected as in wave theory.
• If λ is close to or smaller than the spacing, the photons pass between the atoms; this is how X-rays pass through many materials.

• An electron starting from rest and accelerated through a potential difference V gains kinetic energy equal to the work done by the field:
• e V = ½ m v² (5-7), so v = √(2eV/m).
• Therefore λ = h/√(2 m e V). Numerically (for V in volts): λ ≈ 1.23/√V nm (for example V = 150 V gives 0.10 nm).
• The larger the accelerating voltage, the faster the electron and the shorter its wavelength. (At very high voltages relativistic corrections are needed, but they are not required here.)

1. Classical physics cannot explain phenomena in which light or electromagnetic radiation interacts with electrons and atoms.
2. Radiation consists of photons of energy E = hν = hc/λ, where h = 6.63 × 10⁻³⁴ J·s.
3. Planck curve; Wien’s law λmax ∝ 1/T; Planck solved the problem by quantizing the energy of oscillators (E = nhν).
4. no emission below the threshold frequency; current ∝ intensity (above threshold); KEmax depends on the frequency, not the intensity; emission is instantaneous. Equation: hν = Ew + ½mv²_max, Ew = hνc.
5. A photon has equivalent mass m = hν/c², momentum p = h/λ, and travels at c. It exerts a very small force on a wall (F = 2P_w/c for reflection) but can throw away a free electron.
6. The Compton effect (scattered photon of lower frequency, recoiling electron) proves the particle nature of photons through conservation of energy and momentum.
7. A wave describes the collective behaviour of photons; its intensity measures photon concentration.
8. any particle has a wave with λ = h/mv. The electron microscope is the proof; it has very high resolving power because accelerated electrons have extremely short wavelengths.
9. eV = ½mv².