Photoelectric emission from a given surface of metal can take place when the value of a ‘physical quantity’ is less than the energy of incident photon. The physical quantity is :

Options

A. Threshold frequency
B. Work function of surface
C. Threshold wave length
D. Stopping Potential

Answer

To solve the question regarding the physical quantity that must be less than the energy of the incident photon for photoelectric emission to occur, we can analyze the options provided step by step.

### Step-by-Step Solution:

1. **Understanding Photoelectric Emission**:
- Photoelectric emission occurs when light (photons) strikes a metal surface and causes the emission of electrons. For this process to happen, the energy of the incoming photons must be sufficient to overcome the energy barrier of the metal.

2. **Identifying the Relevant Physical Quantities**:
- The question provides four options: threshold frequency, work function, threshold wavelength, and stopping potential. We need to determine which of these is a physical quantity that must be less than the energy of the incident photon for photoelectric emission to occur.

3. **Analyzing Each Option**:
- **Threshold Frequency (ν₀)**: This is the minimum frequency required for photoelectric emission. The energy of a photon is given by E = hν, where h is Planck's constant. For emission to occur, the frequency of the incident photon must be greater than or equal to the threshold frequency. Therefore, this option does not fit the requirement.

- **Work Function (Φ)**: The work function is the minimum energy required to remove an electron from the metal surface. It is related to the threshold frequency by the equation Φ = hν₀. For photoelectric emission to occur, the energy of the incident photon (E = hν) must be greater than the work function (E > Φ). Hence, the work function must be less than the energy of the incident photon, making this a suitable option.

- **Threshold Wavelength (λ₀)**: This is the maximum wavelength for which photoelectric emission can occur. It is related to the threshold frequency by λ₀ = c/ν₀. While the energy of the photon is inversely related to its wavelength, this option does not directly answer the question regarding the physical quantity that must be less than the energy of the photon.

- **Stopping Potential (V₀)**: This is the potential needed to stop the most energetic photoelectrons emitted. It is related to the kinetic energy of the emitted electrons but does not directly relate to the energy of the incident photon in the context of the threshold for emission.

4. **Conclusion**:
- The most suitable answer is the **work function of the surface (Φ)**, as it is the only physical quantity that must be less than the energy of the incident photon for photoelectric emission to occur.

### Final Answer:
The physical quantity is the **work function of the surface**.