To solve the problem of finding the stopping potential when given the maximum kinetic energy of a photoelectron and the work function of a metal surface, we can use the photoelectric effect equation. Let's break this down step-by-step. ### Step 1: Understand the Photoelectric Effect The photoelectric effect describes how electrons are emitted from a material (usually a metal) when it is exposed to light of sufficient energy. The energy of the incoming photons must overcome the work function (ϕ) of the metal to release electrons. The relationship can be expressed as: \[ E_k = hf - \phi \] Where: - \(E_k\) is the maximum kinetic energy of the emitted photoelectron. - \(hf\) is the energy of the incoming photon (where \(h\) is Planck's constant and \(f\) is the frequency of the light). - \(\phi\) is the work function of the metal. ### Step 2: Relate Kinetic Energy and Stopping Potential The stopping potential (V_s) is the potential difference needed to stop the emitted photoelectrons. The maximum kinetic energy of the photoelectrons can also be expressed in terms of the stopping potential: \[ E_k = eV_s \] Where: - \(e\) is the charge of the electron (approximately \(1.6 \times 10^{-19}\) coulombs). - \(V_s\) is the stopping potential in volts. ### Step 3: Calculate the Stopping Potential From the above equations, we can relate the maximum kinetic energy and the stopping potential: \[ V_s = \frac{E_k}{e} \] However, since we are given the maximum kinetic energy in electron volts (eV), we can directly use the value of \(E_k\) in eV to find \(V_s\): \[ V_s = E_k \] ### Step 4: Substitute the Values Given: - Maximum kinetic energy \(E_k = 0.34 \, \text{eV}\) - Work function \(\phi = 1.83 \, \text{eV}\) We can find the stopping potential: \[ V_s = E_k = 0.34 \, \text{V} \] ### Step 5: Analyze the Options Now, let's look at the options provided: - A. 2.17V - B. 1.49V - C. 1.09V - D. 0.34V The calculated stopping potential is \(0.34 \, \text{V}\), which matches option D. ### Step 6: Why Other Options Are Incorrect - **Option A (2.17V)**: This value is too high and does not correspond to the kinetic energy of the emitted electrons. It suggests a misunderstanding of the relationship between kinetic energy and stopping potential. - **Option B (1.49V)**: This value is also too high and does not reflect the maximum kinetic energy provided in the problem. It could be a miscalculation or misinterpretation of the work function and kinetic energy relationship. - **Option C (1.09V)**: Similar to the previous options, this value does not correspond to the kinetic energy of the emitted electrons and is not derived from the given data. ### Summary - The maximum kinetic energy of the photoelectron is equal to the stopping potential when expressed in electron volts. - The stopping potential is calculated directly from the maximum kinetic energy. - The correct stopping potential is \(0.34 \, \text{V}\), corresponding to option D. - Other options do not align with the calculated stopping potential based on the given kinetic energy. ### Revision Summary - The stopping potential is equal to the maximum kinetic energy of the emitted photoelectron in eV. - Use the formula \(V_s = E_k\) to find the stopping potential. - Ensure to differentiate between work function and kinetic energy when solving photoelectric effect problems. - Always check the units and ensure they are consistent when performing calculations.