Short Answer 
The photoelectric effect requires a photon to have a minimum energy of 5eV to emit an electron, combining the work function of 3eV and an additional energy of 2eV. Using Planck’s equation, the wavelength necessary for this energy is calculated, revealing that option (d) 2875‚àöO is the correct choice as it falls within the required range for photoemission.
Step 1: Understand the Work Function and Photon Energy
To initiate the photoelectric effect, it’s crucial to grasp the concept of the work function, which is the minimum energy needed to release an electron from the surface of a metal. In this case, the work function is 3eV. To emit a photoelectron with an additional energy of 2eV, a photon must provide a total energy of at least 5eV (3eV + 2eV).
Step 2: Apply Planck’s Equation to Find Wavelength
Utilize Planck’s equation, which relates a photon’s energy to its wavelength: E = hc/≈í¬™, where h is Planck’s constant and c is the speed of light. Rearranging this equation to solve for the wavelength, we have: ≈í¬™ = hc/E. First, convert 5eV into joules (1eV = 1.602‚àöo10-19 Joules) before plugging the value into the equation.
Step 3: Determine the Correct Wavelength and Answer
After performing the calculations, the required wavelength will be found to be shorter than 6187‚àöO, establishing that only certain options are viable. Among the provided choices, option (d) 2875‚àöO will emerge as the correct answer since it falls within the needed wavelength range to facilitate the photoemission process effectively.