Photoelectric Effect & Wave Theory of Light 🤔🔆

Key Experimental Findings 🔬

  • For one material and a fixed frequency above threshold, photo-electric current rises in direct proportion to light intensity, yet the stopping potential V0 stays constant 🌟. :contentReference[oaicite:0]{index=0}
  • A sharp threshold frequency n0 exists. If the light frequency is below n0, no electrons pop out—no matter how bright the beam is 🚫. :contentReference[oaicite:1]{index=1}
  • Above n0, the maximum electron energy (or eV0) grows linearly with light frequency n but ignores intensity 📈. :contentReference[oaicite:2]{index=2}
  • Emission kicks in almost instantly (~10−9 s or faster) once n > n0 ⚡. :contentReference[oaicite:3]{index=3}

Why Classical Wave Theory Fails 😵

  • Wave theory predicts electrons soak up energy slowly from the full wave. It would make Kmax climb with intensity and erase any threshold—clashing with real data 🙅. :contentReference[oaicite:4]{index=4}
  • Calculations show a lone electron might need hours to gather escape energy, but experiments see emission right away ⚡. :contentReference[oaicite:5]{index=5}

Einstein’s Photon Picture 🌠

Einstein suggested light arrives in tiny packets called photons. Each carries energy h n (with Planck’s constant h).

  1. An electron absorbs one photon (energy h n).
  2. If h n beats the metal’s work function f0, the electron escapes with:

$$K_{\text{max}} = h\,n – f_0 \tag{11.2}$$

More intense light just means more photons per second—more electrons fly out, but each keeps the same Kmax 😎. :contentReference[oaicite:6]{index=6}

Handy Definitions 📝

  • Threshold frequency n0: the least frequency that can launch electrons; unique for every metal. :contentReference[oaicite:7]{index=7}
  • Work function f0: minimum energy to free an electron; connected by f0 = h n0.
  • Stopping potential V0: reverse voltage that just halts the fastest electrons, so eV0 = Kmax.

Putting It All Together 🚀

  • Kmax vs. frequency is a straight line; slope = ⁄e.
  • Intensity tunes current, not energy.
  • The sharp cut-off stems from the fixed work function.
  • Photon packets make emission immediate and threshold-based.

High-Yield NEET Nuggets 🎯

  1. Einstein’s photo-electric equation \(K_{\text{max}} = h\,n – f_0\).
  2. Meaning and calculation of threshold frequency n0.
  3. V0–frequency graph: slope gives h/e, intercept gives n0.
  4. Intensity controls photo-current; frequency controls electron energy.
  5. Classical wave theory’s failures prove the photon nature of light.