The correct option is **B. Electrons are emitted from a material when it absorbs photons with energy greater than the work function.** ### Detailed Explanation The photoelectric effect is a phenomenon observed when light (or electromagnetic radiation) strikes a material, typically a metal, and causes the emission of electrons from that material. Here’s a step-by-step breakdown of why option B is correct and the other options are incorrect: #### Why Option B is Correct 1. **Photon Energy and Work Function**: - Each photon of light carries energy that is proportional to its frequency, given by the equation: \[ E = h \nu \] where \(E\) is the energy of the photon, \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)), and \(\nu\) is the frequency of the light. - The work function (\(\phi\)) is the minimum energy required to remove an electron from the surface of a material. If the energy of the incoming photon is greater than the work function, the excess energy is converted into kinetic energy of the emitted electron. 2. **Emission of Electrons**: - When a photon with sufficient energy strikes the material, it can transfer its energy to an electron. If this energy exceeds the work function, the electron is emitted from the material. This is a direct observation of the photoelectric effect. 3. **Threshold Frequency**: - There is a specific threshold frequency (\(\nu_0\)) associated with each material, below which no electrons are emitted regardless of the intensity of the light. This threshold frequency is related to the work function by: \[ \phi = h \nu_0 \] #### Why the Other Options are Incorrect **Option A: Light can only be absorbed by matter in continuous waves.** - This statement is incorrect because the photoelectric effect demonstrates that light behaves as a stream of particles (photons) rather than just continuous waves. The quantized nature of light is fundamental to the photoelectric effect, as it is the individual photons that interact with electrons. **Option C: The emission of electrons is independent of the intensity of the incident light.** - This statement is misleading. While the intensity of light (the number of photons hitting the surface per unit time) does not affect the energy of individual photons, it does affect the number of emitted electrons. If the intensity is increased (while keeping the frequency above the threshold), more photons are available to interact with electrons, leading to more electrons being emitted. However, if the frequency is below the threshold, increasing intensity will not result in any electron emission. **Option D: The photoelectric effect can occur with any wavelength of light regardless of energy.** - This statement is incorrect because the photoelectric effect only occurs if the wavelength of the light corresponds to a frequency that provides sufficient energy to overcome the work function. For example, ultraviolet light can cause the photoelectric effect, but visible light may not, depending on the material's work function. ### Summary of Key Points - The photoelectric effect occurs when photons with energy greater than the work function of a material strike it, causing electron emission. - The energy of a photon is given by \(E = h \nu\), and it must exceed the work function for electrons to be emitted. - The intensity of light affects the number of emitted electrons but not their individual energy. - The photoelectric effect is not observed with wavelengths that do not provide sufficient energy to overcome the work function. This understanding of the photoelectric effect is crucial for grasping concepts in quantum physics and the nature of light.