### Correct Option: C ### 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 joules (J) or electronvolts (eV). It represents the energy barrier that must be overcome for an electron to be emitted from the metal. 2. **Energy of Photons**: - Light can be thought of as being made up of particles called photons. The energy (\( E \)) of a single 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. **Condition for Electron Ejection**: - For an electron to be ejected from the metal surface, the energy of the incoming photon must be at least equal to the work function of the metal: \[ h \cdot f \geq \phi \] - The minimum frequency (\( f_0 \)) required to just eject an electron (where the energy of the photon equals the work function) can be derived from the above equation: \[ h \cdot f_0 = \phi \] - Rearranging this gives: \[ f_0 = \frac{\phi}{h} \] - This shows that the minimum frequency of light required to eject electrons is **inversely proportional** to the work function, confirming that option C is correct. ### Why Other Options Are Incorrect: - **Option A: It is directly proportional to the work function.** - This is incorrect because if the frequency were directly proportional to the work function, it would imply that as the work function increases, the frequency also increases. However, the relationship is inverse, as shown in the derivation. - **Option B: It is inversely proportional to the work function.** - While this statement is true, it does not provide the correct formula for calculating the minimum frequency. The correct relationship is given by \( f_0 = \frac{\phi}{h} \), which is more specific and accurate. - **Option D: It is equal to the work function multiplied by Planck's constant.** - This is incorrect because it misrepresents the relationship. The frequency is not obtained by multiplying the work function by Planck's constant; rather, it is derived by dividing the work function by Planck's constant. ### Summary of Key Points: - The photoelectric effect requires a minimum frequency of light to eject electrons from a metal surface. - The relationship between the minimum frequency (\( f_0 \)) and the work function (\( \phi \)) is given by \( f_0 = \frac{\phi}{h} \). - The energy of a photon is calculated using \( E = h \cdot f \). - The work function is a critical factor in determining the minimum frequency needed for electron ejection. This understanding is crucial for solving problems related to the photoelectric effect and for grasping the fundamental principles of quantum physics.