4. (40 POINTS) Below is a energy level scheme of a hypothetical one- electron el

Question

4. (40 POINTS) Below is a energy level scheme of a hypothetical one- electron element Mathematicum. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. (a) (15) How much energy does it take to ionize an electron from the first excited level (n = 2) ? (b) (4) An 8-eV photon is absorbed by a Mathematicum atom in its first excited level. As the atom returns to the first excited level, what possible energies can the emitted photons have? Assume there can be transitions between all pairs of levels, including sub-transitions back to first excited level. (c) (15) What will happen to the atom if a photon of energy of5eV strikes a Mathematicum atom in its first excited state? Explain. (d) (6) What will happen to the aton if a photon of energy of 7 eV strikes a Mathematicum atom in its first excited state? Explain. (e) (15) EXTRA CREDIT: Photons emitted in the Mathemticum transitions n 3 to n = 2 and n 3 to n 1 will eject photoelectrons from a certain metal, but the photons emitted from the transitions n 4 to n = 3 will not, what are the limits (minimum and maximum values) of the work function of the metal? n=4 -S eV n =2 -10 eV =1 20 eV

Explanation / Answer

a) energy of the first excited state = -10eV

so energy of 10eV is needed to ionize

b) the possible transitions are

n=4 to n=3 energy given out = 5 -2 = 3eV

n= 4 to n=2 energy given out = 10 -2 = 8eV

n= 3 t0 n=2 energy given out = 10 -5 = 5eV

hence photons with energies of 3eV, 5eV and 8 eV can be emitted

c) if a photon of 5eV is absorbed , the electron would jump to second excited state that is n=3

d) the photon would not be absorbed as a photon can not be partially absorbed

e) the minimum value of work function is 5 eV

and maximum value of work function is 15eV

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