The correct option is **B. The type of metal used**. ### 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 minimum frequency of light required to eject electrons 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 (Option B) 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 different for different metals. The relationship between the work function and the threshold frequency is given by the equation: \[ \phi = h f_0 \] where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)) and \( f_0 \) is the threshold frequency. 2. **Energy of Photons**: The energy of a photon is given by the equation: \[ E = h f \] where \( E \) is the energy of the photon and \( f \) is its frequency. For electrons to be ejected, the energy of the incoming photons must be equal to or greater than the work function of the metal. Thus, the threshold frequency is directly dependent on the type of metal, as different metals have different work functions. 3. **Example**: For instance, the work function for sodium is about \( 2.3 \, \text{eV} \), which corresponds to a threshold frequency of approximately \( 5.5 \times 10^{14} \, \text{Hz} \). In contrast, for platinum, the work function is about \( 6.3 \, \text{eV} \), leading to a higher threshold frequency. This illustrates how the type of metal determines the threshold frequency. #### Why the Other Options are Wrong or Weaker - **Option A: The intensity of the light**: The intensity of light refers to the number of photons hitting the surface per unit time. While increasing intensity can increase the number of ejected 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. - **Option C: The distance of the light source from the metal**: The distance from the light source can affect 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 distance. - **Option D: The angle of incidence of the light**: The angle at which light strikes the metal surface can influence the distribution of energy among the electrons and may affect the efficiency of electron ejection, but it does not change the threshold frequency. The threshold frequency is determined by the metal's work function, not the angle of incidence. ### Summary - The threshold frequency is the minimum frequency of light required to eject electrons from a metal surface. - It is dependent on the type of metal used, specifically its work function. - Other factors like light intensity, distance from the source, and angle of incidence 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.