Particle Nature of Light: The Photon 🔅

1. Why Think of Light as Particles? 💡

The photoelectric effect showed that light exchanges energy in little packets of size \(h\nu\). Einstein then argued that each packet must also carry momentum \(\displaystyle p=\frac{h\nu}{c}\), so the packet behaves like a particle—later called a photon. Compton’s X-ray-electron scattering in 1924 clinched the idea, and both Einstein (1921) and Millikan (1923) won Nobel Prizes for their work on it. :contentReference[oaicite:14]{index=14}

2. Quick Profile of a Photon 🎯

  • Energy: \(E = h\nu = \dfrac{hc}{\lambda}\) :contentReference[oaicite:15]{index=15}
  • Momentum: \(p = \dfrac{h\nu}{c} = \dfrac{h}{\lambda}\) :contentReference[oaicite:16]{index=16}
  • Speed: always \(c\), the speed of light :contentReference[oaicite:17]{index=17}
  • Energy never depends on the beam’s intensity. Brighter light just means more photons each second. :contentReference[oaicite:18]{index=18}
  • Neutral charge → photons ignore electric and magnetic fields. :contentReference[oaicite:19]{index=19}
  • In any photon–particle clash, total energy and momentum stay conserved (photon count may change). :contentReference[oaicite:20]{index=20}

3. Linking Intensity and Photon Count 🔦

For a beam of power \(P\) at frequency \(\nu\), the number of photons per second is \[ N = \dfrac{P}{h\nu}. \] Brighter beam ⇒ larger \(N\), not larger per-photon energy. :contentReference[oaicite:21]{index=21}

4. Einstein’s Photoelectric Equation ⚡

When a photon hits a metal surface, \[ h\nu = \phi_0 + \tfrac{1}{2} m v_{\text{max}}^2 = \phi_0 + eV_0, \] where

  • \(\phi_0\) is the work function, the minimum energy needed to liberate an electron.
  • \(V_0\) is the stopping potential that just halts the fastest photoelectrons. :contentReference[oaicite:22]{index=22}
The threshold frequency follows directly: \[ \nu_0 = \dfrac{\phi_0}{h}. \quad\text{(Below \(\nu_0\) no electrons emerge.)} \quad :contentReference[oaicite:23]{index=23} \]

5. Worked Examples 📚

Example A (Laser Beam)

A laser emits light at \(\nu = 6.0\times10^{14}\,\text{Hz}\) with power \(2.0\times10^{-3}\,\text{W}\).

  • Photon energy: \(E = h\nu = 3.98\times10^{-19}\,\text{J}\).
  • Photon rate: \(N = P/E = 5.0\times10^{15}\,\text{s}^{-1}\). :contentReference[oaicite:24]{index=24}

Example B (Threshold & Wavelength)

Cesium has \(\phi_0 = 2.14\,\text{eV}\).

  • Threshold frequency: \(\nu_0 = 5.16\times10^{14}\,\text{Hz}\).
  • If a stopping potential \(V_0 = 0.60\,\text{V}\) cancels the current, the incident light’s wavelength is \(454\,\text{nm}\). :contentReference[oaicite:25]{index=25}

6. Momentum Conservation in Photon Collisions 🤝

In events like Compton scattering, energy and momentum both balance: \[ \text{Initial }(E,\,\mathbf p) = \text{Final }(E,\,\mathbf p). \] Photon number may change, but the totals above never budge. :contentReference[oaicite:26]{index=26}

7. High-Yield Nuggets for NEET 🎯

  1. Photon Energy & Momentum: \(E = h\nu\), \(p = h/\lambda\).
  2. Intensity ≠ Energy per Photon: Raising intensity only raises photon count.
  3. Threshold Frequency: \(\nu_0 = \phi_0/h\); no emission below \(\nu_0\).
  4. Einstein’s Equation: \(eV_0 = h\nu – \phi_0\).
  5. Conservation in Photon Collisions: Energy and momentum stay conserved (Compton effect).

Keep these ideas handy, and you’ll ace photon questions in no time! 🌟