Unit 07: Modern Physics • Chapter 11
Photoelectric Effect: Experimental Laws & Apparatus
Work function thresholds, effect of intensity, collector potential, stopping potential ($V_0$), frequency response, instantaneous emission ($< 10^{-9}\text{ s}$), and failure of classical wave mechanics.
Socho ek vending machine ko jisme se chocolate nikaalne ke liye kam se kam ₹10 ka ek single coin dalna zaroori hai. Agar aap ₹1 ke 100 coins bhi le aao, par machine sirf ₹10 ka coin accept karti ho, toh 100 ghante intezar karne ke baad bhi chocolate bahar nahi aayegi!
Classical physics sochte the ki light ek continuous wave hai: agar hum dim light ko bohot der tak metal par chamkayenge ya intense red light dalenge, toh electrons energy ikatthi karke bahar nikal aayenge. Lekin experiment ne hairan kar diya: Chahe kitna bhi powerful red searchlight daalo, ek bhi electron bahar nahi aata, jabki ek nanhi si dim ultraviolet torch chamkate hi turant nano-second ke andar electrons farrate se bahar aane lagte hain! Yeh vending machine ka minimum ₹10 coin hi metal ka Work Function ($\Phi_0$) hai!
1. Work Function & Stopping Potential
Minimum energy and retarding potential definitions:
Stopping potential $V_0$ is completely independent of light intensity! It depends strictly on frequency $\nu$ and work function $\Phi_0$.
2. The 4 Experimental Laws of Photoemission
- Intensity Law: Photoelectric current $I \propto \text{Intensity}$ (for $\nu > \nu_0$).
- Kinetic Energy Law: $K_{\max}$ (and $V_0$) depends linearly on $\nu$, independent of intensity.
- Threshold Law: No emission occurs if $\nu < \nu_0$, regardless of intensity or exposure time.
- Instantaneous Law: Time lag between photon incidence and electron ejection is $< 10^{-9}\text{ s}$.
Collector Potential vs Photoelectric Current Response Curves
Fig 11.1A: Characteristic photoelectric current curves demonstrating stopping potential independence from intensity (Left) and linear dependence on frequency (Right).
1. Saturation Current: When collector plate potential is increased, photoelectric current increases until all emitted photoelectrons are collected; this plateau is the saturation current ($I_{\text{sat}} \propto \text{Intensity}$).
2. Stopping Potential ($V_0$): The minimum negative (retarding) potential applied to the collector plate at which photoelectric current completely drops to zero. At this point, the work done by the retarding electric field stops even the fastest photoelectron with kinetic energy $K_{\max}$:
Trap 1: The Energy Accumulation Prediction Failure
• Wave Theory Prediction: Light wave spreads energy continuously across the entire wavefront. If light is intense enough, electrons should eventually absorb sufficient energy to escape, regardless of frequency.
• Experimental Reality: Below threshold frequency ($\nu < \nu_0$), NO photoelectrons are emitted, even if the light beam is extraordinarily intense (e.g. bright red light on zinc)!
Trap 2: The Time Lag Paradox
• Wave Theory Prediction: A single electron distributed over millions of atoms would take several hours or days to accumulate the work function energy from a wave.
• Experimental Reality: Emission is completely INSTANTANEOUS ($< 10^{-9}\text{ seconds}$)! There is zero measurable time lag because photon-electron collision is an all-or-nothing localized quantum interaction.
Problem: The work function of Cesium is $2.14\text{ eV}$. Find (a) the threshold frequency for cesium, and (b) the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of $0.60\text{ V}$.
Solution: $\Phi_0 = 2.14\text{ eV} = 2.14 \times 1.6 \times 10^{-19}\text{ J} \approx 3.424 \times 10^{-19}\text{ J}$.
1. Threshold frequency ($\nu_0 = \Phi_0/h$):
2. Incident photon energy: $E = \Phi_0 + K_{\max} = \Phi_0 + e V_0$:
Wavelength of incident light:
Work Function
$\Phi_0 = h\nu_0 = \frac{hc}{\lambda_0}$
Stopping Potential
$e V_0 = K_{\max}$
Current Proportionality
$I \propto \text{Intensity}$ ($\nu > \nu_0$)
Emission Delay
$< 10^{-9}\text{ s}$ (Instant)