Photoelectric Effect Concept Check: Assess the truth of two statements about maximum photoelectron energy versus light intensity and frequency.

Introduction / Context:
The photoelectric effect reveals the quantum nature of light. Einstein’s equation relates the maximum kinetic energy of emitted electrons to the frequency of incident light, independent of intensity. This question tests your understanding of how intensity and frequency separately affect photoelectron emission.

Given Data / Assumptions:

• Statement (1): The maximum energy of photoelectrons is independent of light intensity.
• Statement (2): The maximum energy varies nonlinearly with frequency of incident light.
• Material has work function φ; Planck’s constant is h.

Concept / Approach:

Einstein’s photoelectric equation: K_max = h f − φ, where K_max is the maximum kinetic energy and f is the frequency. Intensity affects the number of emitted electrons (current), not their maximum energy, provided f is above threshold f_0 = φ/h.

Step-by-Step Solution:

Verification / Alternative check:

Plot K_max versus f: a straight line cutting the f-axis at f_0 and the K-axis at −φ when extrapolated. Changing intensity shifts the photocurrent magnitude but leaves K_max unchanged.

Why Other Options Are Wrong:

• (1) and (2) both true: contradicts linear dependence on frequency.
• (1) false and (2) true: Intensity does not change K_max; frequency relation is linear, so both parts wrong.
• (1) and (2) both false: (1) is true by Einstein’s equation.
• Insufficient information: The classical relation is well-established; data are sufficient.

Common Pitfalls:

• Confusing intensity (affects number of photoelectrons) with frequency (affects energy of each photoelectron).
• Ignoring threshold frequency; below threshold, no emission regardless of intensity.

Final Answer:

(1) is true and (2) is false