Photoelectric Effect | Structure of Atom Class 11 Notes

The Photoelectric Effect

Structure of Atom | Class 11 Chemistry Notes

1. Introduction & Observations

The Photoelectric Effect is the phenomenon of ejection of electrons from the surface of a metal when light (electromagnetic radiation) of a suitable frequency strikes it.

Key Observations:

• No Time Lag: The ejection of electrons is instantaneous.
• Threshold Frequency ($\nu_0$): For each metal, there is a minimum frequency below which no emission occurs, regardless of intensity.
• Kinetic Energy: Depends on the frequency of incident light, not intensity.
• Number of Electrons: Depends on the intensity (brightness) of incident light.

2. Einstein's Photoelectric Equation

Albert Einstein explained this effect using Planck's Quantum Theory. Energy of photon = Work Function + Kinetic Energy.

$$ h\nu = h\nu_0 + \frac{1}{2}m_e v^2 $$ $$ K_{max} = h\nu - \Phi $$

Where:

• $h\nu$ = Energy of incident photon
• $\Phi$ (or $W_0$) = Work Function ($h\nu_0$)
• $K_{max}$ = Maximum Kinetic Energy of photoelectron
• $\nu_0$ = Threshold Frequency

3. Work Function ($\Phi$)

The minimum energy required to eject an electron from the metal surface. It characterizes the metal.

$$ \Phi = h\nu_0 = \frac{hc}{\lambda_0} $$

Note: Cesium ($Cs$) has the lowest work function, making it useful in solar cells.

4. Stopping Potential ($V_0$)

The minimum negative (retarding) potential applied to the anode that stops even the most energetic photoelectrons.

$$ K_{max} = e \cdot V_0 $$

Therefore, Einstein's equation can be written as:

$$ eV_0 = h\nu - \Phi $$

5. Graphical Analysis

If we plot $K_{max}$ vs Frequency ($\nu$):

• It is a straight line ($y = mx + c$).
• Slope: $h$ (Planck's constant).
• Y-intercept: $-\Phi$ (Negative Work Function).
• X-intercept: $\nu_0$ (Threshold Frequency).

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