Question

In a hypothetical atom, if transition from $n=4$ to $n=3$ produces visible light then possible transition to obtain infrared radiation is :

• A. $n=5$ to $n=3$
• B. $n=4$ to $n=2$
• C. $n=3$ to $n=1$
• D. none of these

Answer 1

Answer: (D)

none of these

Instead of looking at how each electron can make the jump(s) through levels, let’s look at how an electron in a given state can make a single jump. This gives us, from your example,

• For an electron in the 4th level, we have 3 3 single jump possibility, i.e.
  4 →→ 3
  4 →→ 2
  4 →→ 1
• Similarly,
  3 →→ 2
  3 →→ 1
• And finally,
  2 →→ 1

That gives us a total of 3 + 2 + 1 = 6.

If you look at, let’s say 6 levels, you’ll see that the number of possible lines will be of the 5 + … +1 = 15.

So for a jump from kthkth state, the trend can be simplified as ∑${\sum }_{i=1}^{k-1}n$

Maybe not a ‘mathematical’ proof, but this so called proof let me sleep.