(455) HL Photoelectric effect [IB Physics HL]

Overview of the Photoelectric Effect

• The photoelectric effect demonstrates the relationship between light and electricity.

• A photon interacts with a metal surface (e.g., zinc), potentially ejecting electrons, termed photoelectrons.

Key Concepts

Photons

• Definition: Small packets of light energy.

• Photon energy: Given by the equation E = hf (where h is Planck's constant).

Electron Ejection

• Under certain conditions, a photon can cause the emission of electrons when it strikes a metal surface.

• Photoelectric effect: The process wherein photons cause electrons to be emitted from a metal.

Graphical Features

• Expected linear relationship between frequency and emitted electron energy.

• Observed phenomenon: A threshold frequency (f0) below which no electrons are emitted.

• Increasing light intensity does not affect the kinetic energy of the ejected electrons; only photon energy matters.

Threshold Frequency

• Definition: Minimum frequency required to emit electrons from a metal.

• Wavelength and energy relationship: Higher wavelengths correspond to lower energies.

Einstein's Contribution

• Introduced the concept that photon energy is quantized, explaining the threshold frequency.

• Defined work function (φ): The energy necessary to eject an electron from the metal surface.

• Equation relating to maximum kinetic energy of ejected electrons: E_max = hf - φ.

Calculations

Example: Frequency Calculation

• Given photon energy: 2.2 eV.

• Convert energy from eV to joules: 2.2 eV = 3.52 × 10^-19 joules.

• Frequency calculation:

  • Using the equation f = E / h:

  • Frequency f = (3.52 × 10^-19 joules) / (6.63 × 10^-34 J·s) = 5.3 × 10^14 Hz.

Example: Maximum Electron Speed Calculation

• Given work function (φ) for potassium: 1.5 eV.

• Calculate maximum kinetic energy:

  • E_max = hf - φ = 2.2 eV - 1.5 eV = 0.7 eV.

• Convert E_max to joules: 0.7 eV = 1.12 × 10^-19 joules.

• Use kinetic energy formula: E_k = 1/2 mv², solve for speed (v).

  • v = √(2 * E_k / m_e), where m_e is electron mass (9.11 × 10^-31 kg).

  • Resulting speed: v ≈ 4.9 × 10^5 m/s.

Conclusion

• The photoelectric effect and its implications highlight the quantum nature of light and matter.

• Mastery of the subject can simplify exam preparation.