Physics · Dual Nature Of Radiation And Matter · NEET
Caesium has the lowest work function, about 2.14 eV, then Potassium about 2.30 eV, then Sodium about 2.75 eV. Work function is the minimum energy needed to pull an electron out of the metal. A lower work function means the electron is held less tightly, so a smaller photon energy can free it. This is why Cs is used in most photocells - it responds to lower-energy (longer wavelength) light that K and Na cannot handle.
Emission happens only when photon energy is greater than or equal to work function. Compare 2.20 eV to each metal: Cs (2.14 eV): 2.20 is greater than 2.14, so YES it emits. K (2.30 eV): 2.20 is less than 2.30, so NO. Na (2.75 eV): 2.20 is less than 2.75, so NO. So ONLY Caesium emits. This is the exact NEET 2023 question. The trick is that being close (2.20 vs 2.30) still means no emission - there is no partial emission.
Low work function means emission is EASY. Many students flip this. Think of work function as an entrance fee the photon must pay to knock out an electron. A low fee (low work function like Cs) is easy to meet, so electrons come out with even weak light. A high fee (high work function like Na) needs stronger, higher-energy light. So order of ease of emission is: Cs (easiest) > K > Na (hardest).
Threshold wavelength lambda_0 = hc / phi_0 = 1240 / phi_0 (in nm, with phi_0 in eV). A SMALLER work function gives a LONGER threshold wavelength. Cs (2.14 eV): lambda_0 = 1240 / 2.14 = about 580 nm. K (2.30 eV): about 539 nm. Na (2.75 eV): about 451 nm. So Caesium has the longest threshold wavelength - it can be triggered even by yellow-green visible light, while Na needs blue-violet light. Longest threshold wavelength always goes with lowest work function.
Use Einstein's equation: KE_max = E_photon - phi_0. For the same photon energy, subtracting a SMALLER work function leaves MORE kinetic energy. So Cs (smallest phi_0) gives the fastest electrons, then K, then Na (slowest, or no emission at all if E_photon is below its work function). Lowest work function wins twice: it emits with weaker light AND gives higher-energy electrons for the same light.
The work functions of Caesium (Cs), Potassium (K) and Sodium (Na) are 2.14 eV, 2.30 eV and 2.75 eV respectively. If incident electromagnetic radiation has an energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?
The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photoemission from the substance is (approximately):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Caesium has the lowest work function (about 2.14 eV), so it emits photoelectrons even with low-energy visible light. Sodium (2.75 eV) needs higher-energy blue-violet light. Caesium responds to a wider range of light, making it ideal for photocells and light sensors.
Cs (about 2.14 eV) is lowest, then K (about 2.30 eV), then Na (about 2.75 eV) is highest. So the order is Cs < K < Na. Ease of emission is the reverse: Cs (easiest) > K > Na (hardest).
No. Higher work function makes emission HARDER, needing higher photon energy just to start. It does not increase the number of electrons. Number of photoelectrons depends on light intensity (once the frequency is above threshold), not on work function.
List work functions, then keep only metals whose work function is less than or equal to the photon energy. Those emit; the rest do not. For 2.20 eV, only Cs (2.14 eV) qualifies. Ignore how 'close' a value is - the condition is strict.
Use lambda_0 = 1240 / phi_0 in nm. Cs: 1240 / 2.14 = about 580 nm. K: 1240 / 2.30 = about 539 nm. Na: 1240 / 2.75 = about 451 nm. Caesium has the longest threshold wavelength, so it works with the widest range of light.
