### Correct Option: D ### Detailed Explanation: The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when it is exposed to light of sufficient frequency. The key concept here is the **work function** (denoted as \( \phi \)), which is the minimum energy required to remove an electron from the surface of the metal. 1. **Understanding the Work Function**: - The work function is a characteristic property of each metal and is measured in electron volts (eV). It represents the energy barrier that must be overcome for an electron to be emitted from the metal surface. 2. **Energy of Photons**: - Light can be thought of as being made up of particles called photons. The energy (\( E \)) of a photon is given by the equation: \[ E = h \cdot f \] where: - \( E \) is the energy of the photon, - \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), - \( f \) is the frequency of the light. 3. **Threshold Frequency**: - The minimum frequency of light required to eject an electron is known as the **threshold frequency** (\( f_0 \)). This frequency is related to the work function by the equation: \[ \phi = h \cdot f_0 \] - Rearranging this gives us: \[ f_0 = \frac{\phi}{h} \] - This shows that the threshold frequency is directly proportional to the work function. 4. **Condition for Electron Ejection**: - For an electron to be ejected from the metal surface, the energy of the incoming photon must be greater than or equal to the work function: \[ h \cdot f \geq \phi \] - This means that the frequency of the light must be at least equal to the threshold frequency: \[ f \geq f_0 \] - Therefore, the frequency must exceed the threshold frequency defined by the work function. ### Why Other Options Are Incorrect: - **Option A: The frequency is directly proportional to the work function.** - This is misleading. While the threshold frequency is related to the work function, the statement implies that the frequency of light itself is directly proportional to the work function, which is not correct. The frequency must exceed a certain value (the threshold frequency) to eject electrons. - **Option B: The frequency is inversely proportional to the work function.** - This is incorrect. The relationship is not inverse; rather, the threshold frequency is derived from the work function. A higher work function corresponds to a higher threshold frequency, not an inverse relationship. - **Option C: The frequency must be equal to the work function.** - This is incorrect because the work function is measured in energy units (eV), while frequency is measured in hertz (Hz). They are not directly comparable in this way. The frequency must be equal to or greater than the threshold frequency, which is derived from the work function. ### Summary for Revision: - The photoelectric effect requires light of a certain frequency to eject electrons from a metal surface. - The work function is the minimum energy needed to remove an electron, related to the threshold frequency by \( \phi = h \cdot f_0 \). - The frequency of light must exceed the threshold frequency (\( f_0 \)) to eject electrons. - The correct answer is that the frequency must exceed the threshold frequency defined by the work function (Option D).