Effect of Wavelength on the Work Function in the Photoelectric Effect
Question:
According to Einstein, as the wavelength of the incident monochromatic light beam becomes shorter, the work function of a target material in a phototube:
- A. increases
- B. decreases
- C. remains constant
- D. is directly proportional to wavelength
Answer:
Understanding Einstein’s Photoelectric Equation
The photoelectric effect is governed by Einstein’s equation:
Where:
- Kmax = Maximum kinetic energy of emitted electrons
- h = Planck’s constant
- c = Speed of light
- λ = Wavelength of incident light
- φ = Work function of the material
Key Concept: Work Function φ
The work function φ is a fixed property of the material. It represents the minimum amount of energy needed to liberate an electron from the surface. It is determined by the atomic structure of the material and does not depend on the wavelength or energy of the incident photons.
Effect of Wavelength
As the wavelength λ of the incident light becomes shorter, the energy of each photon increases because:
A shorter wavelength implies a higher photon energy, which results in a greater kinetic energy for emitted electrons. However, since φ is constant, the threshold for electron emission stays unchanged regardless of wavelength.
Conclusion:
According to Einstein’s photoelectric theory, the work function is an intrinsic property of the target material. Therefore, changes in wavelength only affect the energy delivered to the electrons—not the amount of energy needed to release them. So, the correct answer is: