The energy-level scheme for the hypothetical one-electron element Searsium is sh

Question

The energy-level scheme for the hypothetical one-electron element Searsium is shown in the figure . The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. Photons emitted in the Searsium transitions n = 3 - > n = 2 and n = 3 - > n = 1 will eject photoelectrons from an unknown metal, but the photon emitted from the transition n = 4 - > n = 3 will not. What is the maximum possible value of the work function of the metal?

Explanation / Answer

The energy of the respective photons emitted by the transitions are E(4->3)= 3eV E(3->2)= 5eV E(3->1)= 15eV since the photon of 5eV energy is able to eject photoelectrons while another with 3eV energy can't...the Maximum value of the work function shall be 5eV. Note:if the electron with 5eV of energy can emit photoelectrons then the one with 15 eV obviously can too. hence we chose the one with the lower energy as the maximum limit.

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