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 and minimum possible values of the work function of the metal? Express answer to one significant figure.

I've tried to use both = h f and = = hf - E(k max) but the work function is always wrong. If someone could explain how to do this would be much appreciated.

Explanation / Answer

Energy released in n->3 to n-> 2 transition = -5 - (-10 ) = 5eV

energy released in n= 3 -> n=1 transition = -5 - (-20 ) = 15 eV

energy released in n= 4 -> n=3 transition = -2 - (-5 ) = 3 eV

So , the energy of 3 eV is not sufficient to eject photoelectrons so , it is the minimum work function of the unknown metal .

Whereas an energy of 5 eV is sufficient to eject photoelectrons so , it is the maximum work function of unknown metal as beyond this energy level we have photoelectron ejection .

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