A metal has a work function of 3.0 eV. What is the threshold frequency of the metal when electrons are just…

Analyze the question: We need the threshold frequency f₀ of a metal whose work function is 3.0 eV. At the threshold, the photon energy equals the work function, so the electrons are just liberated with zero kinetic energy.

Concept: Einstein's photoelectric equation is hf = φ + KE. At threshold KE = 0, so

φ = hf₀, which gives f₀ = φ / h

Solution:

1. Convert the work function to joules: φ = 3.0 × 1.6 × 10⁻¹⁹ = 4.8 × 10⁻¹⁹ J

2. Divide by Planck's constant: f₀ = (4.8 × 10⁻¹⁹) / (6.6 × 10⁻³⁴) f₀ = 0.727 × 10¹⁵ Hz f₀ ≈ 7.3 × 10¹⁴ Hz

Check against the options:

• A is the work function in joules, not a frequency.
• C (4.8 × 10¹⁴) is what you would get by dividing 4.8 by 10 instead of by 6.6.
• D (7.3 × 10¹⁴ Hz) matches my result.

Tip: For threshold frequency questions, always do two things: convert eV to joules (multiply by 1.6 × 10⁻¹⁹), then divide by h. Check that your answer is in the 10¹⁴ to 10¹⁵ Hz range, which is typical for visible and UV light. That alone eliminates options A and B.