Chemistry · Structure Of Atom · NEET
If an electron is in shell number n and falls down to the ground state (n=1), the maximum number of different spectral lines is n(n-1)/2. Here n is the highest level the electron starts from. This is the total count of all possible downward jumps.
A spectral line comes from ONE jump between two levels. From level n the electron can drop to many lower levels, and from each of those it can drop again. So you must count every possible pair of levels. The number of ways to pick 2 levels out of n is n(n-1)/2. That is why it is not simply n.
Put n=4 into the formula: 4(4-1)/2 = 4x3/2 = 6 lines. The 6 jumps are 4to3, 4to2, 4to1, 3to2, 3to1, and 2to1. Each jump gives one line of a fixed colour or wavelength.
No. A series is a group of lines that all END on the same lower level (like Lyman ends on n=1, Balmer ends on n=2). The total NUMBER of lines is n(n-1)/2, but these lines are shared among several series. Do not confuse total lines with number of series.
Then use the general form: number of lines = (n2 - n1)(n2 - n1 + 1)/2, where n2 is the upper level and n1 is the lower level it stops at. If it always ends at the ground state (n1=1), this simplifies to n(n-1)/2.
Yes. Each downward jump releases a photon of a fixed energy, and that fixed energy means a fixed wavelength (colour). Since every pair of levels has a different energy gap, every line has a different wavelength. That is why counting lines matters for NEET.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is n(n-1)/2 when the electron falls to the ground state (n=1). For example n=6 gives 6x5/2 = 15 lines.
n(n-1)/2 = 6(6-1)/2 = 15 spectral lines.
Use (n2 - n1)(n2 - n1 + 1)/2, where n2 is the upper level and n1 is the lower level. If n1=1 this becomes n2(n2-1)/2.
From n=2 the only possible jump is 2 to 1, so there is just one line. The formula 2(2-1)/2 = 1 confirms this.
The counting formula n(n-1)/2 works for any single-electron atom or ion (like He+ or Li2+), because it only counts possible jumps, not the atom type. The wavelengths differ, but the number of lines is the same.
