Homework #10
Conceptual Solution

1. (b) For the Bohr atom, the energy levels are

   

   Here the ground state energy level, with n=1, has , so that and Z=2, corresponding to He. Since it is a one electron ion, the He must be singly ionized, .

2. (d) Again, the energy levels are , so

   

3. (a) The ionization energy is the energy required to remove the electron from its usual, ground state (n=1) from the potential well of the atom, giving it final energy zero so that it is not trapped inside the atom. This is just minus , or 54.4 eV.
4. (c) Since for a photon , the photon with the longest wavelength has the smallest energy. This occurs for the transition with the smallest energy change between initial and final electron energy levels (since the photon carries the difference in those 2 energies). That transition is C, between levels 3 and 4.
5. (b) Transition E goes from electron atomic energy level 2 to 3, requiring absorption of a photon with energy

   

6. (e) Transition A goes from electron atomic energy level 2 to 1, emitting a photon with energy

   

   To obtain the momentum of the photon, we recall that

   

   for the photon, since its obeys (which is not true for massive particles). Converting into SI units and dividing by c gives

   

7. (b) A photon is emitted when the electron gives off energy in the transition, by dropping to a lower energy level; a photon is absorbed in providing the energy for an electron to raise its energy level to a higher level. In transitions A and B, the electron gives off energy by emitting a photon; while in C, D, and E, it gains energy by absorbing a photon.

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