Question

How many many more spectral lines can be there in transition from third energy levels which 1 is equal to to first energy level and second one

Answer 1

$$\begin{gathered} Noofspectrallinesifitfallstosecondleveli.e.,n_1=2from{n}_2=3means \\ =\frac{(n_2-n_1)\left(\right(n_2-n_1+1)}{2}=\frac{(3-2)(3-2+1)}{2}=\frac{1\times 2}{2}=1line \\ Noofspectrallinesifitfallstofirstleveli.e.,n_1=1from{n}_2=2means \\ =\frac{n(n-1)}{2}=\frac{2(2-1)}{2}=\frac{2}{2}=1line \end{gathered}$$