FAD1022 L44 — Photons and Photoelectric Effect

This lecture covers the concept of photons as discrete packets of light energy and the photoelectric effect as experimental proof of light's particle nature.

Lecture File

  • Lecture 44 - Photons and Photoelectric Effect.pdf (29 slides)
  • Lecturer: Nurul Izzati (NIA)

Key Topics

1. Photon — Definition & Properties

A photon is the smallest packet (quantum) of electromagnetic radiation (light energy). It demonstrates that light exhibits wave-particle duality.

Key Properties:

  • Elementary particle of light with no charge
  • Always travels at speed of light in vacuum: $c = 3.00 \times 10^8$ m/s
  • Massless particles (no resting mass)
  • Carry both energy and momentum
  • Exhibit wave-particle duality

2. Photon Energy Equations

The energy of a photon depends on its frequency and wavelength:

$$E = hf = \frac{hc}{\lambda}$$

Where:

  • $E$ = energy of photon (J)
  • $h$ = Planck's constant = $6.63 \times 10^{-34}$ J·s
  • $f$ = frequency (Hz)
  • $c$ = speed of light = $3.0 \times 10^8$ m/s
  • $\lambda$ = wavelength (m)

Key Relationships:

  • Higher frequency → Higher photon energy
  • Shorter wavelength → Higher photon energy

Examples:

  • Gamma rays: very high frequency → very high energy
  • Radio waves: low frequency → low energy
  • X-rays: short wavelength → high energy
  • Red light: longer wavelength → lower energy

3. Historical Evolution of Light Theory

Scientist Contribution View
Max Planck (1900) Energy released in "chunks" or "quanta", $E = hf$ Math trick (not physical)
Albert Einstein (1905) Light itself is made of physical chunks called "light quanta" Physical reality
Modern Term These chunks are called photons Discrete packets of wave energy

4. The Photoelectric Effect

Definition: The emission of electrons from a metal surface when light of suitable frequency shines on it. The emitted electrons are called photoelectrons.

Why Classical Wave Theory Failed:

  • Classical physics predicted stronger light (higher intensity) should always eject electrons
  • But experiments showed low frequency bright light cannot eject electrons, while high-frequency dim light can

Einstein's Photon Explanation:

  • Light consists of photons
  • Each photon carries energy $E = hf$
  • One photon transfers energy to one electron (one-to-one interaction)

5. Work Function & Threshold Frequency

Work Function ($\phi$): The minimum energy needed to remove an electron from the metal surface.

Threshold Frequency ($f_0$): The minimum frequency of light needed to eject electrons:

$$f_0 = \frac{\phi}{h}$$

Three Cases:

Condition Result
$hf < \phi$ No electron emitted
$hf = \phi$ Electron escapes with zero kinetic energy
$hf > \phi$ Electron emitted with kinetic energy

6. Einstein's Photoelectric Equation

$$KE_{max} = hf - \phi$$

Where:

  • $KE_{max}$ = maximum kinetic energy of ejected electron
  • $hf$ = photon energy
  • $\phi$ = work function

7. Role of Intensity vs. Frequency

Property Controls
Frequency WHETHER electrons are emitted (energy per photon)
Intensity HOW MANY electrons are emitted (number of photons)

8. Stopping Potential ($V_s$)

The minimum voltage needed to stop the most energetic photoelectrons:

$$KE_{max} = eV_s$$

Where $e$ = electron charge

Example Problems

Example 1: Calculate energy of a photon with frequency $6 \times 10^{14}$ Hz

$$E = hf = 6.63 \times 10^{-34} \times 6 \times 10^{14} = 3.98 \times 10^{-19} \text{ J}$$

Example 2: Determine wavelength of photon with energy $3.0 \times 10^{-19}$ J

$$\lambda = \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{3.0 \times 10^{-19}} = 6.626 \times 10^{-7} \text{ m}$$

Example 3 (from slides): Electrons are ejected from a metallic surface with speeds ranging up to $4.6 \times 10^5$ m/s when light with a wavelength of $\lambda = 625$ nm is used.

(a) What is the work function of the surface? (b) What is the cutoff frequency for this surface?

Solution (a):

$$KE_{max} = \frac{1}{2}m_e v_{max}^2 = \frac{1}{2}(9.11 \times 10^{-31})(4.6 \times 10^5)^2 = 9.6 \times 10^{-20} \text{ J}$$

$$\phi = \frac{hc}{\lambda} - KE_{max} = \frac{(6.63 \times 10^{-34})(3.00 \times 10^8)}{625 \times 10^{-9}} - 9.6 \times 10^{-20} = 2.2 \times 10^{-19} \text{ J} = \boxed{1.4 \text{ eV}}$$

Solution (b):

$$f_c = \frac{\phi}{h} = \frac{2.2 \times 10^{-19}}{6.63 \times 10^{-34}} = \boxed{3.3 \times 10^{14} \text{ Hz}}$$

Example 4 (from slides): When light of wavelength 350 nm falls on a potassium surface, electrons are emitted that have a maximum kinetic energy of 1.31 eV. Find:

(a) the work function of potassium, (b) the cutoff wavelength, and (c) the frequency corresponding to the cutoff wavelength.

Solution (a):

$$\phi = \frac{hc}{\lambda} - KE_{max} = \left(\frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{350 \times 10^{-9}} \times \frac{1 \text{ eV}}{1.60 \times 10^{-19}}\right) - 1.31 \text{ eV} = \boxed{2.24 \text{ eV}}$$

Solution (b):

$$\lambda_c = \frac{hc}{\phi} = \left(\frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{2.24 \text{ eV}} \times \frac{1 \text{ eV}}{1.60 \times 10^{-19}}\right) = \boxed{555 \text{ nm}}$$

Solution (c):

$$f_c = \frac{c}{\lambda_c} = \frac{3.00 \times 10^8}{555 \times 10^{-9}} = \boxed{5.41 \times 10^{14} \text{ Hz}}$$

Applications

  • Solar Panels — photon energy conversion
  • Fiber Optics — light transmission via photons
  • Lasers — coherent photon emission
  • Phototherapy — medical applications

Diagrams

Photoelectric Effect Decision Tree

graph TB
    A[("Photoelectric Effect")] --> B{"Compare hf and phi"}
    B -->|"hf < phi"| C["No Electrons Emitted"]
    B -->|"hf = phi"| D["Electrons Escape with KE = 0"]
    B -->|"hf > phi"| E["Electrons Emitted with KE = hf - phi"]
    
    C --> C1["Increase Frequency or Change Metal"]
    E --> E1["Intensity Controls Number of Electrons"]
    E --> E2["Frequency Controls Whether Emission Occurs"]
    
    style A fill:#e7f5ff,stroke:#1971c2
    style C fill:#ffe3e3,stroke:#c92a2a
    style D fill:#fff4e6,stroke:#e67700
    style E fill:#d3f9d8,stroke:#2f9e44

Historical Evolution of Light Theory

graph LR
    A["Planck (1900)"] --> B["Einstein (1905)"]
    B --> C["Modern Term: Photon"]
    
    A --> A1["Energy in Quanta"]
    B --> B1["Light Made of Physical Quanta"]
    C --> C1["Discrete Packets of Wave Energy"]
    
    style A fill:#ffe8cc,stroke:#d9480f
    style B fill:#c5f6fa,stroke:#0c8599
    style C fill:#d3f9d8,stroke:#2f9e44

Related Concepts

Lecturer

Nurul Izzati (NIA) — PASUM Physics Lecturer

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