To determine the minimum frequency of light required to cause the photoelectric effect in a material with a work function of 3.0 eV, we can use the relationship between energy, frequency, and Planck's constant. The photoelectric effect occurs when light of sufficient energy strikes a material and causes the ejection of electrons. The energy of the incoming photons must be equal to or greater than the work function of the material for this to happen. ### Step-by-Step Explanation 1. **Understanding Work Function**: - The work function (\( \phi \)) is the minimum energy required to remove an electron from the surface of a material. In this case, \( \phi = 3.0 \, \text{eV} \). 2. **Energy of a Photon**: - The energy (\( E \)) of a photon can be calculated using the formula: \[ E = h \cdot f \] where: - \( E \) is the energy of the photon in electron volts (eV), - \( h \) is Planck's constant (\( 4.14 \times 10^{-15} \, \text{eV·s} \)), - \( f \) is the frequency of the light in hertz (Hz). 3. **Setting Up the Equation**: - To find the minimum frequency (\( f_{\text{min}} \)) that can cause the photoelectric effect, we set the energy of the photon equal to the work function: \[ h \cdot f_{\text{min}} = \phi \] - Rearranging this gives: \[ f_{\text{min}} = \frac{\phi}{h} \] 4. **Substituting Values**: - Now, substituting the known values into the equation: \[ f_{\text{min}} = \frac{3.0 \, \text{eV}}{4.14 \times 10^{-15} \, \text{eV·s}} \] 5. **Calculating the Frequency**: - Performing the calculation: \[ f_{\text{min}} = \frac{3.0}{4.14 \times 10^{-15}} \approx 7.24 \times 10^{14} \, \text{Hz} \] 6. **Rounding and Comparing with Options**: - The calculated frequency \( 7.24 \times 10^{14} \, \text{Hz} \) is closest to option B, which is \( 7.0 \times 10^{14} \, \text{Hz} \). ### Evaluating the Options - **Option A: \( 5.0 \times 10^{14} \, \text{Hz} \)**: - This frequency is too low to provide the necessary energy to overcome the work function of 3.0 eV. Thus, it cannot cause the photoelectric effect. - **Option B: \( 7.0 \times 10^{14} \, \text{Hz} \)**: - This is the correct answer as it is the closest to our calculated minimum frequency of \( 7.24 \times 10^{14} \, \text{Hz} \). - **Option C: \( 1.0 \times 10^{15} \, \text{Hz} \)**: - While this frequency is sufficient to cause the photoelectric effect, it is not the minimum frequency required. Therefore, it is not the correct answer. - **Option D: \( 6.0 \times 10^{14} \, \text{Hz} \)**: - This frequency is also too low to provide the necessary energy to overcome the work function of 3.0 eV. ### Summary - The minimum frequency of light required to cause the photoelectric effect is calculated using the work function and Planck's constant. - The correct answer is \( 7.0 \times 10^{14} \, \text{Hz} \) (Option B). - Frequencies lower than this value cannot provide enough energy to eject electrons from the material. - Always ensure to compare calculated values with given options to select the closest match. ### Revision Summary - The work function is the minimum energy needed to eject electrons. - Use \( E = h \cdot f \) to relate energy and frequency. - Calculate minimum frequency using \( f_{\text{min}} = \frac{\phi}{h} \). - The correct answer is \( 7.0 \times 10^{14} \, \text{Hz} \) (Option B).