The correct option is **C. The kinetic energy of emitted electrons increases linearly with the frequency of the incident light above a certain threshold frequency.** ### Detailed Explanation: 1. **Understanding the Photoelectric Effect**: - The photoelectric effect is a phenomenon where electrons are emitted from a material (usually a metal) when it is exposed to light (or electromagnetic radiation) of sufficient frequency. This effect was crucial in establishing the particle nature of light and led to the development of quantum mechanics. 2. **Key Concepts**: - **Threshold Frequency (f₀)**: This is the minimum frequency of light required to eject electrons from the surface of a material. If the frequency of the incident light is below this threshold, no electrons will be emitted, regardless of the intensity of the light. - **Kinetic Energy of Emitted Electrons (KE)**: When light of frequency \( f \) (greater than the threshold frequency) strikes the material, the energy of the incoming photons is given by the equation: \[ E = hf \] where \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \, \text{Js} \)). 3. **Energy and Kinetic Energy Relationship**: - The energy of the incoming photon must overcome the work function (\( \phi \)) of the material to release an electron. The work function is the minimum energy needed to remove an electron from the surface of the material. - The kinetic energy of the emitted electron can be expressed as: \[ KE = hf - \phi \] - This equation shows that the kinetic energy of the emitted electrons increases linearly with the frequency of the incident light, as long as the frequency is above the threshold frequency. 4. **Why Option C is Correct**: - As the frequency \( f \) increases beyond the threshold frequency \( f₀ \), the term \( hf \) increases, leading to a greater kinetic energy \( KE \) of the emitted electrons. This linear relationship is a direct consequence of the equation \( KE = hf - \phi \). ### Analysis of Other Options: - **Option A**: "The kinetic energy of emitted electrons decreases as the frequency of the incident light increases." - This statement is incorrect because, according to the photoelectric effect, increasing the frequency of light (beyond the threshold) increases the energy of the photons, which in turn increases the kinetic energy of the emitted electrons. - **Option B**: "The kinetic energy of emitted electrons is independent of the frequency of the incident light." - This is also incorrect. The kinetic energy is directly dependent on the frequency of the incident light, as shown in the equation \( KE = hf - \phi \). If the frequency changes, the kinetic energy changes accordingly. - **Option D**: "The kinetic energy of emitted electrons is proportional to the intensity of the incident light regardless of its frequency." - This statement is misleading. While the intensity of light (which is related to the number of photons) can affect the number of emitted electrons, it does not affect the kinetic energy of the electrons. The kinetic energy is determined solely by the frequency of the light, not its intensity. ### Summary: - The photoelectric effect demonstrates that light can behave as a particle (photons). - The threshold frequency is crucial for electron emission; below it, no electrons are emitted. - The kinetic energy of emitted electrons increases linearly with the frequency of incident light above the threshold frequency. - The intensity of light affects the number of emitted electrons but not their kinetic energy. ### Revision Summary: - The photoelectric effect involves the emission of electrons from a material when exposed to light. - The threshold frequency is the minimum frequency needed to emit electrons. - Kinetic energy of emitted electrons increases linearly with frequency above the threshold. - Intensity affects the number of emitted electrons, not their kinetic energy.