Photoelectric Effect Notes, Graphs, Numericals & PYQs

1. Photoelectric Effect

Early experiments revealed light-induced electron emission from metal surfaces.

Definition

Photoelectric effect is the emission of electrons from a material surface when electromagnetic radiation of sufficient frequency falls on it.

Energy Transfer

One photon transfers its energy hν to one electron. Part overcomes the work function and the remainder becomes kinetic energy.

Instantaneous Emission

Energy is delivered in a single photon-electron interaction, so no classical accumulation time is required.

Historical Experiments

Hertz observed UV-assisted spark discharge; Hallwachs observed loss of negative charge from illuminated zinc.

2. Photoelectric Emission

Work Function

Φ = hν₀

Minimum surface escape energy; depends on material and surface condition.

Threshold Frequency

ν₀ = Φ/h

No emission occurs for ν < ν₀, regardless of intensity.

Threshold Wavelength

λ₀ = c/ν₀ = hc/Φ

Emission requires λ ≤ λ₀.

Electron Escape

Surface electrons need less energy to escape than deeply bound electrons; emitted electrons therefore have a range of kinetic energies.

3. Experimental Setup

Evacuated photoelectric tube with illuminated cathode, collecting anode, variable potential and microammeter.

The variable battery can accelerate electrons toward the anode or reverse the field to retard them. The microammeter measures collected photoelectric current in the evacuated tube.

4. Experimental Observations

Threshold

Every cathode material has a minimum frequency ν₀.

No Time Lag

Emission begins essentially as soon as suitable light arrives.

Intensity

Higher intensity increases current by increasing photon flux.

Frequency

Higher frequency increases Kmax and stopping potential.

Energy Range

Electrons emerge with energies from nearly zero up to Kmax.

Saturation

At sufficiently positive anode potential, all emitted electrons are collected.

5. Threshold Frequency

Definition

The least frequency capable of liberating electrons from a given surface.

ν₀ = Φ/h

Threshold Wavelength

λ₀ = hc/Φ

For λ > λ₀, emission is impossible.

Example

For Φ = 2.0 eV, λ₀ = 1240/2.0 = 620 nm.

Concept Trap

Increasing intensity below ν₀ only adds more low-energy photons; it cannot cause emission.

6. Stopping Potential

Einstein Equation

hν = Φ + KmaxKmax = hν − Φ

Stopping Relation

Kmax = eV₀hν = Φ + eV₀

Physical Meaning

V₀ is the reverse potential just sufficient to prevent even the fastest photoelectrons from reaching the anode.

Dependence

V₀ rises linearly with frequency and is independent of intensity.

7. Saturation Current

Saturation current is directly proportional to incident intensity above threshold frequency.

Saturation current is reached when every emitted photoelectron is collected. It increases with photon flux and therefore with intensity, but its ideal value is not controlled by stopping potential.

8. Effect of Intensity

Increasing intensity raises saturation current; stopping potential remains unchanged.

At fixed ν > ν₀, greater intensity means more photons per second, more emitted electrons and larger saturation current. Photon energy, Kmax and V₀ stay unchanged.

9. Effect of Frequency

Increasing frequency makes stopping potential more negative while saturation current stays fixed for constant intensity.

At fixed intensity, increasing frequency increases photon energy and makes the stopping potential larger in magnitude. In the idealised comparison, saturation current remains the same.

10. All Important Graphs

Increasing intensity raises saturation current; stopping potential remains unchanged.

Increasing frequency makes stopping potential more negative while saturation current stays fixed for constant intensity.

Kmax = hν − Φ: slope h and threshold-frequency x-intercept ν₀.

V₀ = (h/e)ν − Φ/e; the intercept on the frequency axis is ν₀.

Saturation current is directly proportional to incident intensity above threshold frequency.

11. Laws of Photoelectric Emission

Law 1

For each metal, emission occurs only when ν ≥ ν₀.

Law 2

Photoelectric current is proportional to incident intensity above threshold.

Law 3

Kmax and stopping potential depend on frequency, not intensity.

Law 4

Emission begins without measurable time lag.

Law 5

At fixed frequency and intensity, current reaches saturation at sufficient positive potential.

50 Conceptual Questions

C1. What is photoelectric emission?

Answer: Electron emission caused by incident electromagnetic radiation.