Question

What is meant by threshold wavelength \( \lambda_0 \) and threshold frequency \( \nu_0 \) in photoelectric effect? On which factors do the saturation current and the value of cut-off voltage depend?

Hint:

Remember: Saturation current depends on light intensity, whereas cut-off voltage is determined by light frequency and the material's work function.

Answer 1

Step 1: Threshold Wavelength and Threshold Frequency Threshold Wavelength: Threshold wavelength \( \lambda_0 \) is the longest wavelength of incident light that can cause photoemission. It is related to the work function \( \phi \) of the material by the equation: \[ \lambda_0 = \frac{hc}{\phi} \] If the wavelength \( \lambda \) of the incident light is greater than \( \lambda_0 \), photoemission does not occur. 

Threshold Frequency: Threshold frequency \( \nu_0 \) is the minimum frequency of the incident light required to eject electrons from the metal surface. It is given by: \[ \nu_0 = \frac{\phi}{h} \] If the frequency \( \nu \) of the incident light is less than \( \nu_0 \), no photoelectric emission occurs. \[ \boxed{\lambda_0 = \frac{hc}{\phi}, \quad \nu_0 = \frac{\phi}{h}} \] \

Step 2: Factors affecting Saturation Current and Cut-off Voltage Saturation Current: Saturation current is the maximum current obtained when all photoelectrons emitted from the surface reach the anode.

 It depends on: - Intensity of Incident Light: As the intensity increases, more photons strike the surface, resulting in the emission of more electrons. \[ \text{Saturation current} \propto \text{Intensity of light} \]

 Cut-off Voltage: Cut-off voltage (stopping potential) is the minimum negative potential required to stop the photoelectrons from reaching the anode. 

It depends on: - Frequency of Incident Light: Higher frequency photons carry more energy, requiring a higher cut-off voltage to stop the electrons. Using Einstein's photoelectric equation: \[ eV_{\text{cut-off}} = h\nu - \phi \] \[ \boxed{\text{Saturation current} \propto \text{intensity}, \quad V_{\text{cut-off}} \propto \text{frequency.}} \]