A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal?

Question

BlackTom AI · Accepted Answer

We are told the metal has a work function φ = 2.50 eV. For photoemission to occur, the photon energy E = hc/λ must be at least φ. The longest wavelength that can cause emission is the threshold wavelength where E = φ, so λ_max = hc/φ.

Using the common value hc ≈ 1240 eV·nm, we get λ_max ≈ 1240 / 2.50 ≈ 496 nm. This means wavelengths around 496 nm are just energetic enough to overcome the work function.

Now evaluate each option:
- 797 nm: photon energy E = 1240/797 ≈ 1.56 eV, which is less than φ. Insufficient energy to overcome the work function, so no emission occurs.
- 397 nm: photon energy E = 1240/397 ≈ 3.13 eV, which is greater than φ. Emission will occur, and electrons will have kinetic energy of roughly E − φ ≈ 0.63 eV.
- 197 nm: photon energy E = 1240/197 ≈ 6.30 eV, well above φ. Emission will occur with substantial kinetic energy, about 6.30 − 2.50 ≈ 3.80 eV.
- 497 nm: photon energy E = 1240/497 ≈ 2.50 eV, essentially equal to φ. This is the threshold case, so emission is possible with near-zero kinetic energy.

Therefore, among the choices, 497 nm corresponds to the longest wavelength that can just eject electrons, while the shorter-wavelength options would also eject electrons but at higher photon energies.

A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal?Single choice

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