What requirement must be met for light to result in the ejection of an electron?

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For light to cause the ejection of an electron from a material—a phenomenon known as the **photoelectric effect**—a specific requirement related to the energy of the incoming light must be met. This requirement is based on the following key principle:

### **Minimum Photon Energy (Threshold Frequency)**

- **Photon Energy Requirement:** Each photon of the incident light must possess **sufficient energy** to overcome the **work function** (φ) of the material. The work function is the minimum energy needed to eject an electron from the surface of the material.

- **Relation to Frequency:** The energy of a photon is directly proportional to its frequency (ν) and is given by the equation:
  
  $$
  E = h \nu
  $$
  
  where:
  
  - $$ E $$ is the energy of the photon,
  - $$ h $$ is Planck's constant ($$6.626 \times 10^{-34} \, \text{J·s}$$),
  - $$ \nu $$ is the frequency of the light.

- **Threshold Frequency ($$ \nu_{\text{threshold}} $$):** This is the minimum frequency required for photons to have enough energy to eject electrons. It is defined by:
  
  $$
  h \nu_{\text{threshold}} = \phi
  $$
  
  If the frequency of the incident light ($$ \nu $$) is:
  
  - **Greater than $$ \nu_{\text{threshold}} $$:** Photons have enough energy to eject electrons, potentially with some kinetic energy leftover.
  - **Less than $$ \nu_{\text{threshold}} $$:** Photons lack sufficient energy, and no electrons are ejected regardless of the light's intensity.

### **Key Takeaway**

**The incident light must have a frequency equal to or higher than the material’s threshold frequency, ensuring each photon carries enough energy (hf ≥ φ) to overcome the work function and eject an electron.**

This means that only light with sufficiently high frequency—such that each photon’s energy meets or exceeds the material’s work function—can result in the ejection of electrons.

**References:**
- Photoelectric Effect, Quantum Physics
- Work Function and Threshold Frequency Concepts
For light to eject an electron, each photon must have enough energy to overcome the material's work function. This means the light must have a frequency equal to or higher than the material's threshold frequency.

What requirement must be met for light to result in the ejection of an electron?

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