The correct option is **B. The type of metal used**. ### Detailed Explanation: The photoelectric effect is a phenomenon where electrons are emitted from a metal surface when it is exposed to light of sufficient frequency. The minimum frequency of light required to eject electrons from the surface of a metal is known as the **threshold frequency** (denoted as \( f_0 \)). This threshold frequency is fundamentally linked to the properties of the metal itself. #### Why the Answer is Correct: 1. **Work Function**: Each metal has a characteristic property called the **work function** (\( \phi \)), which is the minimum energy required to remove an electron from the surface of that metal. The work function is related to the threshold frequency by the equation: \[ \phi = h f_0 \] where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)). This equation shows that the threshold frequency is directly dependent on the work function, which varies from one metal to another. 2. **Different Metals, Different Thresholds**: Different metals have different work functions due to their atomic structure and the binding energy of their electrons. For example, metals like cesium have a low work function and thus a low threshold frequency, while metals like platinum have a higher work function and a correspondingly higher threshold frequency. This means that the type of metal directly determines the minimum frequency of light needed to emit electrons. #### Why the Other Options are Wrong or Weaker: - **A. The intensity of the light**: The intensity of light refers to the amount of energy per unit area per unit time. While increasing the intensity can increase the number of emitted electrons (if the frequency is above the threshold), it does not affect the threshold frequency itself. The threshold frequency is solely determined by the metal's work function, not the intensity of the light. - **C. The distance from the light source**: The distance from the light source affects the intensity of light reaching the metal surface (due to the inverse square law), but it does not change the frequency of the light. The threshold frequency is a property of the metal and remains constant regardless of how far the light source is from the metal. - **D. The temperature of the metal**: While temperature can affect the kinetic energy of the emitted electrons (higher temperatures can lead to more energetic electrons), it does not change the threshold frequency. The threshold frequency is determined by the work function of the metal, which is a fixed property at a given state of the metal. ### Summary of Key Points: - The threshold frequency is the minimum frequency of light required to emit electrons from a metal surface. - It is determined by the work function of the metal, which varies between different metals. - The intensity of light, distance from the light source, and temperature of the metal do not affect the threshold frequency. - Understanding the relationship between work function and threshold frequency is crucial for grasping the photoelectric effect. This understanding is essential for students preparing for exams in physics, particularly in topics related to quantum mechanics and the photoelectric effect.