Physics

Physics

Problem

Identify the correct relation connecting the work function ϕ\phi, Planck constant hh, speed of light cc, and threshold wavelength λ0\lambda_0 of a photosensitive surface. a) ϕ=hc2 λ0\phi = \dfrac{h c}{2\,\lambda_0} b) ϕ=2hcλ0\phi = \dfrac{2 h c}{\lambda_0} c) ϕ=hcλ0\phi = \dfrac{h c}{\lambda_0} d) ϕ=3hc2 λ0\phi = \dfrac{3 h c}{2\,\lambda_0}
Intuitive explanation

The work function is the minimum energy needed to free an electron from a metal surface—and that energy comes from a photon. The key insight is that at the threshold wavelength λ0\lambda_0, a photon carries just enough energy to do this job with nothing left over. Use the photon energy formula E=hfE = hf and the wave relation c=λfc = \lambda f to connect the photon's energy to its wavelength, then set it equal to the work function.

Intuitive explanation

The work function is the minimum energy needed to free an electron from a metal surface—and that energy comes from a photon. The key insight is that at the threshold wavelength λ0\lambda_0, a photon carries just enough energy to do this job with nothing left over. Use the photon energy formula E=hfE = hf and the wave relation c=λfc = \lambda f to connect the photon's energy to its wavelength, then set it equal to the work function.

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