Short Answer

Threshold frequency is the minimum frequency of incident light required to eject electrons from a metal surface in the photoelectric effect. If the light frequency is below this value, no electrons are emitted, no matter how intense the light is.

It depends on the work function of the metal, which is the minimum energy needed to remove an electron. The relationship is given by:

where   is the work function,   is Planck’s constant, and   is the threshold frequency.

Detailed Explanation :

Threshold Frequency in Photoelectric Effect

The threshold frequency is a fundamental concept in the photoelectric effect, which occurs when light strikes a metal surface and causes emission of electrons. According to Einstein’s photoelectric equation:

•  = kinetic energy of emitted electrons
•  = Planck’s constant
•  = frequency of incident light
•  = work function of the metal

The threshold frequency ( ) is the frequency at which the kinetic energy of the emitted electron becomes zero. At this point, the photon energy is just sufficient to overcome the work function:

• Light with frequency less than   cannot eject electrons, regardless of its intensity.
• Light with frequency greater than   emits electrons with kinetic energy  .

Factors Affecting Threshold Frequency

1. Type of Metal:
   • Each metal has a unique work function, so   varies for different metals.
   • For example:
     • Sodium:   Hz
     • Potassium:   Hz
2. Work Function ( ):
   • Represents the minimum energy needed to release an electron from the metal surface.
3. Wavelength Relation:
   • Threshold frequency is inversely related to threshold wavelength ( ):

where   is the speed of light. Longer wavelength light has lower energy and may not exceed the threshold.

Importance of Threshold Frequency

1. Explains Photoelectric Phenomenon:
   • Demonstrates why electrons are emitted only for light above a certain frequency, not intensity.
2. Confirms Particle Nature of Light:
   • Photon energy depends on frequency ( ), supporting Einstein’s explanation.
3. Material Identification:
   • Helps determine the work function of metals by measuring threshold frequency.
4. Technological Applications:
   • Important in photoelectric cells, photodetectors, and solar panels, ensuring efficient electron emission.

Experimental Observation

• Light of varying frequency is directed at a metal surface.
• If  , no electrons are emitted.
• If  , electrons are emitted instantly with kinetic energy proportional to  .
• Increasing light intensity below   does not produce emission, confirming the concept of threshold frequency.

Conclusion

Threshold frequency is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect. It depends on the work function of the metal and is crucial for explaining why electron emission occurs only above certain frequencies. The concept supports the particle nature of light and has practical applications in photoelectric cells, solar panels, and photodetectors. Understanding threshold frequency is essential in both theoretical and applied physics.