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The Existence of a Threshold
Photoelectric emission is a fundamental quantum effect, responsible for turning light into the electrons that matter. Among its major features, startling enough, is the existence of a threshold frequency, which indicates the absence of a photoelectric emission process for a specified material. In this article, we will look at the threshold frequency, its importance, and the reason as to why it exists in detail.
What is Threshold Frequency?
The threshold frequency (( f_{\text{threshold}} )) is the lowest frequency of incident radiation able to liberate electrons from the surface of a material by means of the photoelectric process. As long as the frequency of light is lower than this threshold, no electrons are emitted irrespective of the intensity of light. This trend is quite at variance with the classical wave approach which surmised that raising the intensity of light should result in the emission of electrons.
In energy terms, the relationship is expressed as:
\( E_{\text{photon}} = hf \)
Where:
- \( E_{\text{photon}} \): Energy of the incident photon
- \( h \): Planck’s constant (\( 6.626 \times 10^{-34} \, \text{J·s} \))
- \( f_{\text{threshold}} \): Threshold frequency
If the photon energy (( hf )) is less than the material’s work function (( \phi )), ejection of electrons does not happen.
Explanation for Threshold Frequency
The threshold frequency stems from the notion of the work function (( \phi )), which is defined as the minimum energy needed to free an electron from the surface of a material. Photoelectric emission occurs only if:
\( hf \geq \phi \)
1. Energy Quantization
Light consists of energy in discrete packets known as photons, each with energy ( E = hf ). An electron on the surface of a substance can absorb the energy of one photon. If the photon’s energy is less than the work function, the electron does not have enough energy to overcome the binding forces of the material.
2. Material Dependence
The work function of a material is determined by its electronic structure and surface properties. For example:
- Sodium has a relatively low work function (\( \phi \approx 2.3 \, \text{eV} \)).
- Platinum has a high work function (\( \phi \approx 5.6 \, \text{eV} \)).
The corresponding threshold frequencies for these materials are given by:
\( f_{\text{threshold}} = \frac{\phi}{h} \)
Significance of Threshold Frequency
1. Determines Material Suitability
To exhibit photoelectric emission, a material must be exposed to light of a wavelength corresponding to a frequency above the threshold frequency. For instance:
- High work-function materials require ultraviolet light (\( \lambda < 400 \, \text{nm} \)).
- Low work-function materials like alkali metals can emit electrons with visible light.
2. Implications for Quantum Theory
The threshold frequency reinforces the quantum nature of light. Classical theories predicted that increasing light intensity should always cause emission, but experiments show that frequency is the decisive factor.
3. Practical Applications
The threshold frequency forms the basis for technologies like:
- Photoelectric cells: Used in solar panels, light sensors, and automatic doors.
- Spectroscopy: Identifying materials based on their threshold frequencies.
Experimental Evidence
1. Hertz and Hallwachs’ Observations: In the late 19th century, Heinrich Hertz and Wilhelm Hallwachs observed that light caused electron emission from metals only above certain frequencies.
2. Einstein’s Explanation: In 1905, Albert Einstein explained that photons must have energy (( hf \geq \phi )) sufficient to eject electrons.
3. Millikan’s Validation: Millikan’s precise experiments confirmed Einstein’s theory, validating the existence of the threshold frequency.
How Does Frequency Affect Kinetic Energy of Electrons?
When ( f > f_{\text{threshold}} ), the kinetic energy of the emitted electrons is given by:
\( K.E_{\text{max}} = hf – \phi \)
Key observations:
- Higher Frequency: Leads to an increase in \( K.E_{\text{max}} \), causing faster ejected electrons.
- Lower Frequency: Prevents emission entirely, regardless of light intensity.
Conclusion
The threshold frequency is a pivotal concept in the photoelectric effect, marking the transition from classical to quantum physics. It highlights the quantized nature of light and provides insights into material properties. Understanding threshold frequency has led to advancements in technology and fundamental physics, shaping fields from renewable energy to spectroscopy.
Next time you operate a solar-powered device or light-sensitive equipment, remember: the threshold frequency makes it all possible!
This question appeared in the “Physics Class 12 CBSE Question Paper 2024 – Section C“
