To solve the problem, we need to understand the photoelectric effect, which describes how light can liberate electrons from a metal surface. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Given Information - **Energy of the incident light (E)**: 5 eV - **Work function of the metal (Φ)**: 3 eV ### Step 2: Calculate the Kinetic Energy of the Liberated Electrons When light of energy \( E \) strikes a metal surface, it can liberate electrons if the energy is greater than the work function \( Φ \). The excess energy is converted into the kinetic energy (KE) of the emitted electrons. The kinetic energy of the emitted electrons can be calculated using the formula: \[ KE = E - Φ \] Substituting the given values: \[ KE = 5 \, \text{eV} - 3 \, \text{eV} = 2 \, \text{eV} \] ### Step 3: Relate Kinetic Energy to Stopping Potential The stopping potential \( V_s \) is the potential difference needed to stop the most energetic photoelectrons. The relationship between the kinetic energy of the electrons and the stopping potential is given by: \[ KE = eV_s \] where \( e \) is the charge of an electron (approximately 1.6 x \( 10^{-19} \) coulombs). Since we are working in electron volts (eV), we can directly equate the kinetic energy in eV to the stopping potential in volts: \[ V_s = KE \] Thus, substituting the kinetic energy we calculated: \[ V_s = 2 \, \text{V} \] ### Conclusion: Identify the Correct Option The stopping potential is therefore 2 V. Looking at the options provided: - A. 1.7V - B. 2.0V - C. 8.0V - D. 15.0V The correct answer is **B. 2.0V**. ### Step 4: Explanation of Incorrect Options - **Option A (1.7V)**: This value is less than the calculated stopping potential. It does not account for the full kinetic energy of the emitted electrons. - **Option C (8.0V)**: This value is much higher than the calculated stopping potential. It suggests a misunderstanding of the energy balance in the photoelectric effect. - **Option D (15.0V)**: This value is also significantly higher and does not relate to the energies given in the problem. It implies an incorrect interpretation of the work function and incident light energy. ### Summary of Key Points - The energy of the incident light must exceed the work function to liberate electrons. - The excess energy becomes the kinetic energy of the emitted electrons. - The stopping potential is equal to the kinetic energy of the electrons in volts. - The correct stopping potential in this case is 2.0V, corresponding to option B. ### Revision Summary - Understand the photoelectric effect and the role of work function. - Calculate kinetic energy using \( KE = E - Φ \). - Relate kinetic energy to stopping potential using \( KE = eV_s \). - The stopping potential in this case is 2.0V, confirming option B as correct.