If we have a one-electron atom, and the electron can occupy any of 5 different energy levels, and transitions are possible between any level and any other, how many lines might appear in that atom's spectrum?

10

Explanation:

Lets say that a, b, c, d, e are the five allowed energy states in order of decreasing energy. Then the number of possible different spectral lines comes from the electron dropping from a high state to a lower state. So, they will do so in following ways:

a - b

a - c

a - d

a - e

b - c

b - d

b - e

c - d

c - e

d - e

Ans - Ten different possible energy jumps giving six different colors or lines in the spectrum.