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

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