Photoelectric effect energy relation: With frequency n, threshold frequency n0, and constant k, the photoelectron energy satisfies

Introduction / Context:
The photoelectric effect demonstrates that light energy is quantized. Electrons are emitted from a material when incident photons carry sufficient energy. The linear relationship between photon frequency and photoelectron kinetic energy is a cornerstone of quantum theory and remote sensing detector physics.

Given Data / Assumptions:

• Incident photon frequency is n, material threshold frequency is n0.
• Constant k corresponds to Planck's constant h when energy is expressed in joules.
• Work function equals k * n0.

Concept / Approach:
Einstein's photoelectric equation is E = h n − Φ, where Φ is the work function. Writing Φ = h n0 and replacing h by a generic constant k gives E = k (n − n0). Emission occurs only for n ≥ n0; otherwise, no electrons are ejected regardless of light intensity.

Step-by-Step Solution:
Start with E = h n − Φ.Set Φ = h n0.Replace h with k (as given): E = k (n − n0).Conclude linear dependency with slope k and threshold at n0.

Verification / Alternative check:
Plotting stopping potential versus frequency yields a straight line with slope h/e and intercept −n0, experimentally confirming the relation.

Why Other Options Are Wrong:
E = k (n + n0): Would imply higher threshold increases energy at fixed n—physically incorrect.E = k (n * n0): Nonlinear and dimensionally inconsistent.E = 0 for all n: Contradicts observations above threshold.E = k / (n − n0): Inverse relation not supported by experiment.

Common Pitfalls:
Confusing intensity with frequency; increasing intensity below threshold never causes emission, while frequency governs emission onset and energy.

Final Answer:
E = k (n - n0).