Question

If an atom had 5 energy levels, how many possible different emission lines could it emit?

Answer 1

There's no easy way to tell. The wavelenght of an emission line is determined by the energy *difference* between energy levels. So you get as many wavelengths (lines) as you have different-sized energy gaps.

If the levels are spaced like this:

Then you'd have six lines, in order from longest to shortest wavelength:

(1) E->D, D->C, or B->A.

(2) E->C.

(3) C->B.

(4) D->B or C->A.

(5) D->A.

(6) E->A.

Answer 2

Whoops, forgot E->B in case (5).

Answer 3

So, what is the answer?

Answer 4

I don't have an answer for you. You have to say how the energy levels are arranged.

Let's see. How about if we assume the energy levels are all equally spaced? That would be the most common case, because it correspond to simple harmonic motion.
In that case, you have four lines:

(1) transitions between neighboring levels, e.g. E->D, D->C, C->B, B->A.

(2) transitions between next nearest neighbors, e.g. E->C, D->B, C->A.

(3) transitions skipping two levels, e.g. E->B, D->A.

(4) transitions skipping three levels, e.g. E->A.

Or we could assume no gaps between energy levels are the same, as in the H atom. Then we get:

(a) 4 lines for transitions down from the highest level to the four lower levels.

(b) 3 lines for the transitions from the next-highest level to the three lower levels.

(c) 2 lines for the transitions from the middle level down to the lower two.

(d) 1 line for the transition from the second level to the lowest.

Total of 10 lines.

Answer 5

Ok, thank you. I will come back to rate once I submit my answer and receive the outcome. I appreciate the breakdown of information.