Question

The work functions of Caesium (Cs), Potassium (K) and Sodium (Na) are 2.14eV, 2.30 eV and 2.75eV respectively. If incident electromagnetic radiation has an incident energy of 2.20eV, which of these photosensitive surfaces may emit photoelectrons?

• A. Na only
• B. Cs only
• C. Both Na and K
• D. K only

Answer 1

The Correct Option is B

The question involves the study of the photoelectric effect, which is the emission of electrons from a metal surface when light of a certain frequency shines on it. The work function (\(\phi\)) is the minimum energy needed to remove an electron from the surface of the material.

To determine which photosensitive surfaces can emit photoelectrons when exposed to electromagnetic radiation with a given energy, we compare the incident energy with the respective work functions.

1. Understanding Work Functions: The work function for each metal is provided:
   • Caesium (Cs): \(2.14 \text{ eV}\)
   • Potassium (K): \(2.30 \text{ eV}\)
   • Sodium (Na): \(2.75 \text{ eV}\)
2. Incident Energy: The energy of the incident electromagnetic radiation is \(2.20 \text{ eV}\).
3. Comparison with Work Functions: For photoemission to occur, the energy of the incident radiation must be greater than or equal to the work function of the material:
   • For Caesium (Cs): \(2.20 \text{ eV} > 2.14 \text{ eV}\). Therefore, Cs can emit photoelectrons.
   • For Potassium (K): \(2.20 \text{ eV} < 2.30 \text{ eV}\). Therefore, K cannot emit photoelectrons.
   • For Sodium (Na): \(2.20 \text{ eV} < 2.75 \text{ eV}\). Therefore, Na cannot emit photoelectrons.
4. Conclusion: Based on the comparison, only Caesium (Cs) can emit photoelectrons when exposed to the given incident electromagnetic radiation.

Hence, the correct answer is Cs only.