The energies, E, for the first few states of an unknown element are shown here in arbitrary units.

Question

n 1 2 3 4 0
E -63 -27 -12 9 infinity
A gaseous sample of this element is bombarded by photons of various energies (in these same units). Match each photon to the result of its absorption (or lack thereof) by an n=1 electron.
Photon Energy Results
A 63 ?
B 51
C 47
D 36

Answer 1

The electron is in n=1 now and if the energy is right it will move to one of the upper energy levels. Take the difference between n=1 and the others; ;i.e.,
n=1 = -63
n=2 = -27
-63-(-27) = -36 so it will take 36 units to move to n = 2. D has 36 units so D will move to n = 2. The others are done the same way. Don't worry about the - sign; that occurs because of convention.