When a metallic surface is illuminate with radiation of wavelength , the stopping potential is . If the same surface is illuminated with radiation of wavelength , the stopping potential is . The threshold wavelength for the metallic surface is:
Step 1: Given data
For case 1,
For case 2,
Step 2: Equation for the energy
Here, is the wavelength, is the planks constant, is the velocity of light, is the threshold wavelength, and is the phase difference.
2. For the second case.
.Step 3: Calculation of the threshold wavelength
Dividing the first equation by the second equation.
Hence, the threshold wavelength for the metallic surface is .
Therefore, option (D) is correct.