Dual Nature of Radiation and Matter Class 12 Notes

Photoelectric Effect

• For a given metal there is a threshold frequency
• $\nu_0$
• below which no electrons are emitted, however intense the light.
• The maximum kinetic energy of emitted electrons depends on the frequency, not the intensity, of light.
• The number of emitted electrons per second (the photocurrent) is proportional to the intensity.
• Emission is nearly instantaneous — there is no meaningful time lag.

Einstein's Photoelectric Equation

• Photon energy:
• $E = h\nu = \frac{hc}{\lambda}$
• .
• Photon momentum:
• $p = \frac{h}{\lambda}$
• .
• Above the threshold:
• $K_{\max} = h\nu - \phi_0$
• ; below it no current flows at any intensity.

Stopping Potential and Graphs

• Slope of the V₀–ν graph:
• $\frac{h}{e}$
• .
• Different metals give parallel lines with the same slope but different intercepts (work functions).
• The saturation photocurrent rises with intensity at fixed frequency.

Wave Nature of Matter — de Broglie

• Heavy or fast objects have tiny wavelengths — that is why macroscopic matter shows no observable wave behaviour.
• Increasing the accelerating voltage decreases the electron wavelength.
• Momentum of a photon can also be written
• $p = \frac{h\nu}{c}$
• .

Davisson-Germer Experiment

• The effect appears only for certain accelerating voltages, where the de Broglie wavelength satisfies the diffraction condition.
• It confirms the wave nature of matter and completes the particle–wave duality of electrons.

Solved Examples

Example: A metal has a work function of 2.0 eV. Light of wavelength 400 nm falls on it. Find the maximum kinetic energy of the emitted electrons.

Solution: Photon energy $E = \frac{hc}{\lambda} = \frac{1240\,\text{eV\,nm}}{400\,\text{nm}} = 3.1\,\text{eV}$. Then $K_{\max} = 3.1 - 2.0 = 1.1\,\text{eV}$. The electrons are released, so the photoelectric effect occurs.