Photo Electric Effect Compact with PYQ

phy-1109 PHY-1109 Physics

1. Definition and Experimental Setup

• Definition: The phenomenon where electrons are emitted from a metal surface when light of a sufficiently high frequency falls upon it. This discovery occurred late in the nineteenth century.
• Experimental Observation: The effect is typically observed using an evacuated tube containing two electrodes connected to a source of variable voltage. The metal plate being irradiated acts as the anode. Photoelectrons emerging from this surface may reach the cathode (despite its negative polarity) and constitute the measured current.
• Stopping Potential ($V_0$): This is the certain value of repulsive voltage (order of several volts) required to stop the photoelectrons, causing the current to drop to zero.
  • The stopping potential ($V_0$) corresponds to the maximum photoelectron kinetic energy ($T_{max}$).
  • The relationship is: ${\mathbf{T}}_{\mathbf{max}}=\mathbf{e}{\mathbf{V}}_0$.

PYQ	Year(s) of Appearance
Photoelectric effect: diagrams showing variation of (i) photoelectric current vs potential difference for three intensities, (ii) photoelectric current vs stopping potentials for three frequencies.	2021
Define photoelectric current, work function, threshold frequency, phase velocity, and group velocity.	2022

2. Failure of Classical Electromagnetic (EM) Wave Theory

Classical EM wave theory failed to explain three key experimental findings.

Classical Prediction (Incorrect)	Experimental Observation
Time Lag: Since energy is spread across wavefronts, a period of time should elapse for an electron to accumulate enough energy (several eV) to leave the metal.	No Time Lag: There is virtually no time interval (within $\sim 10^{-9}$ s) between the light arrival and the emission of photoelectrons.
Intensity Dependence: Increasing the intensity of light should increase the energy of the electrons.	Intensity vs. Number: A brighter light yields more photoelectrons, but the electron energies remain the same, provided the frequency is constant.
Frequency Dependence: Emission should occur regardless of frequency, as long as intensity is sufficient.	Threshold Frequency (${\nu }_0$): Electrons are only emitted if the light frequency ($\nu$) is above a certain critical frequency (${\nu }_0$) characteristic of the metal. The maximum kinetic energy increases linearly with frequency.

PYQ	Year(s) of Appearance
What is photoelectric effect? What are the limitations of classical electromagnetic wave to explain it?	2017, 2019
Discuss the drawbacks of classical physics in explaining photoelectric effect.	2019

3. Einstein’s Quantum Theory and Photoelectric Equation

In 1905, Einstein proposed that the energy in light is concentrated in small packets called photons, rather than spread out over wavefronts. The term “photon” was coined later in 1926 by Gilbert Lewis.

Key Concepts & Formulae:

1. Work Function ($\varphi$ or $h{\nu }_0$):

   • The minimum energy needed to dislodge an electron from a particular metal surface.
   • It is related to the threshold frequency (${\nu }_0$) by the formula: $\varphi =\mathbf{h}{\nu }_0$.
   • The work function ($\varphi$) and threshold frequency (${\nu }_0$) vary depending on the metal.

2. Einstein’s Photoelectric Equation: The energy of the incident photon ($h\nu$) is used partly to dislodge the electron (work function, $h{\nu }_0$) and partly to give the electron kinetic energy ($T_{max}$).

   $\mathbf{h}\nu ={\mathbf{T}}_{\mathbf{max}}+\mathbf{h}{\nu }_0$

   Where:

   • $h\nu$: Energy content of the incident light photon.
   • $T_{max}$: Maximum photoelectron energy.
   • $h{\nu }_0$: Work function of the metal.
   • $h$: Planck’s constant ($6.63\times 10^{-34}\text{ joule}\cdot \text{sec}$), which is always the same regardless of the metal.

Explaining Experimental Laws using Quantum Theory:

Einstein’s hypothesis resolves the classical contradictions:

1. Instantaneous Emission: Since the energy is concentrated in a photon, the electron absorbs all the required energy instantly (if $\nu >{\nu }_0$), resulting in no delay.
2. Intensity vs. Energy: All photons of frequency $\nu$ have the same energy $h\nu$. Increasing light intensity only changes the number of photons, thus changing the number of photoelectrons emitted, but not their individual energies.
3. Frequency vs. Energy: A higher frequency ($\nu$) means a greater photon energy ($h\nu$), resulting in more energy imparted to the photoelectrons. If $h\nu$ is less than $h{\nu }_0$, no electron is emitted, regardless of intensity.

PYQ
What is the photo electric effect? Write down the Einsteins hypothesis about photoelectric effect.
Derive Einstein’s photo-electric equation and explain the laws of photoelectric emission.

4. Photoelectric Numerical Questions (PYQs)

Numerical PYQ	Year(s) of Appearance
The photoelectric threshold frequency of silver is $0.86\times 10^{15}$ Hz. Calculate (i) the maximum kinetic energy, (ii) the stopping potential for $4\times 10^{15}$ Hz UV light.	2019
Metal threshold wavelength $6000\text{A˚}$. Calculate stopping potential when irradiated with (i) monochromatic light $\lambda =4000\text{A˚}$, (ii) light having twice the intensity and frequency.	2024