The work function of a substance is 3.0 eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

Solution

Physics sir · 3 steps

The longest wavelength is the one whose photon carries exactly the work function, and not a bit more.

1. Threshold condition. A photon of wavelength λ carries energy hc/λ. A longer wavelength means less energy, so the longest useful wavelength λ₀ gives a photon energy exactly equal to the work function φ.

   λ₀ = hc/φ

2. Put in numbers. hc = 6.63 × 10⁻³⁴ × 3 × 10⁸ = 1.989 × 10⁻²⁵ J m, and φ = 3.0 × 1.6 × 10⁻¹⁹ = 4.8 × 10⁻¹⁹ J. So λ₀ = (1.989 × 10⁻²⁵)/(4.8 × 10⁻¹⁹) = 4.14 × 10⁻⁷ m.
3. So. λ₀ ≈ 414 nm, which is option (c). Any wavelength longer than this cannot eject electrons.

The idea to keep. Remember hc ≈ 1240 eV nm. Then λ₀ (nm) = 1240/φ (eV), and the threshold wavelength takes you two seconds.

Answer from the NTA final answer key. Solution by PrepWiser.