Question

How many lines are produced when an electron jumps from the fifth to the second orbit for a hydrogen atom?

• A. 8
• B. 10
• C. 15
• D. 6

Hint:

Count all the orbits between the start and end level, then work out how many pairs of orbits that gives.

Answer 1

The Correct Option is D

Step 1: When an electron falls from a higher orbit to a lower orbit, it does not have to jump in one shot. It can also stop at any orbit lying in between, on its way down to the final orbit. So we must count every orbit that lies between the starting orbit and the final orbit, both included. Here the electron starts at \(n_2 = 5\) and ends at \(n_1 = 2\). The orbits involved are \(n = 2, 3, 4, 5\), which is 4 orbits in total.
Step 2: Every pair of these orbits gives one spectral line, since a line is produced for every possible jump between two levels. The number of ways to choose 2 orbits out of \(n\) orbits is \[\dfrac{n(n-1)}{2}\]
Step 3: Put \(n = 4\): \[\dfrac{4 \times 3}{2} = \dfrac{12}{2} = 6\]
So the electron cascading from the 5th orbit down to the 2nd orbit produces 6 spectral lines.
\[\boxed{6 \text{ spectral lines}}\]