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(Figure 1) . The potential energy is taken to be zero for an electron at an infinite distance from the nucleus.

A)How much energy (in electron volts) does it take to ionize an electron from the ground level?

B)

An 18.0eVphoton is absorbed by a searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels.

Answer in paragraph.

C) What will happen if a photon with an energy of 8.00

eV strikes a searsium atom in its ground level? Why?
Answer in paragraph.
D)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 are the limits (maximum and minimum possible values) of the work function of the metal?
Answer in the order indicated. Separate your answers with a comma.
?min,?max

Explanation / Answer

A
20 eV
This is the energy you need to raise level from -20eV (at n=1)
to 0eV (at n? infinity)

B
By absorbing 18eV the electron reaches the state n=4.
Th electron returns to state n=1 by one ore more of the following steps by emitting the energy ?E
n=4 ? n=3 ?E?? = 3eV
n=3 ? n=2 ?E?? = 5eV
n=4 ? n=2 ?E?? = 8eV
n=2 ? n=1 ?E?? = 10eV
n=3 ? n=1 ?E?? = 15eV
n=4 ? n=1 ?E?? = 18eV

C
Nothing will happen.
To change the the state from n=1 you need at least 10eV, to change to state n=2 (or more for reaching a higher state).

D
The work function ? equals the minimum energy of a photon to remove a electron from the metal.

For n=4 ? n=3 with E_photon = 3eV the energy is too low.
For n=3 ? n=2 with E_photon = 5eV and n=3 ? n=1 with E_photon = 15eV photoelectric effect occurs. Hence the minimum energy of the photoelectric effect is somewhere between 3eV and 5eV:
3eV < ? ? 5eV

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