Photons & Photoelectric effect - 2 | Early Quantum Theory

E_k = hν - hν₀  (photoelectric effect)
At the longest wavelength that can eject an electron: ν = ν₀

E₀ = hν₀  where E₀ is the minimum energy to eject one electron from silver (in J).
E₀ = $\frac{\mathrm{E}}{{\mathrm{N}}_{\mathrm{A}}}$ = $\frac{412 \times {10}^3 \mathrm{J}.{\mathrm{mol}}^{-1}}{6.022 \times {10}^{23} {\mathrm{mol}}^{-1}}$ = 6.84 x 10^-19 J.

E₀ = hν₀ = $\frac{\mathrm{hc}}{{\mathrm{\lambda }}_0}$

⇒ λ₀ = $\frac{\mathrm{hc}}{{\mathrm{E}}_0}$ where λ₀ is the longest wavelength that can eject an electron.

⇒ λ₀ = 291 nm