Question

{"given":"Threshold wavelength: $\\lambda_0 = 5200\\ \\text{Å}$. Condition for photoelectric emission: $\\lambda_{\\text{incident}} < \\lambda_0$","key_observation":"For photoelectric emission to occur, the wavelength of incident light must be less than the threshold wavelength ($\\lambda < \\lambda_0$). The power or intensity of the source only affects the rate of electron emission — it does NOT determine whether emission occurs at all. Only the photon energy (i.e., wavelength/frequency) determines whether the threshold condition is met.","option_analysis":[{"label":"(A)","text":"50 W infrared lamp","verdict":"incorrect","explanation":"Infrared light has wavelengths typically in the range $7000\\ \\text{Å}$ to $10^6\\ \\text{Å}$, which is greater than $5200\\ \\text{Å}$. Since $\\lambda_{\\text{IR}} > \\lambda_0$, infrared photons have insufficient energy to cause photoemission, regardless of the lamp's power."},{"label":"(B)","text":"1 W infrared lamp","verdict":"incorrect","explanation":"Like option (A), infrared light has wavelengths greater than $5200\\ \\text{Å}$, so it cannot cause photoelectric emission. Reducing the power from 50 W to 1 W does not change this conclusion."},{"label":"(C)","text":"50 W ultraviolet lamp","verdict":"correct","explanation":"Ultraviolet light has wavelengths typically in the range $100$–$4000\\ \\text{Å}$, which is less than $5200\\ \\text{Å}$. Since $\\lambda_{\\text{UV}} < \\lambda_0$, each UV photon carries sufficient energy to eject electrons, satisfying the photoelectric emission condition."},{"label":"(D)","text":"1 W ultraviolet lamp","verdict":"correct","explanation":"Ultraviolet light satisfies $\\lambda_{\\text{UV}} < 5200\\ \\text{Å}$ regardless of the lamp's power. Even a 1 W UV lamp emits photons with energy exceeding the work function, so photoelectric emission will occur (though at a lower rate than with 50 W)."}],"answer":"(C) and (D)","formula_steps":[]}