來曼系

萊曼系

${\displaystyle {1 \over \lambda }=R\left({1 \over 1^{2}}-{1 \over n^{2}}\right)\qquad \left(R=1.0974\times 10^{7}{\mbox{m}}^{-1}\right)}$

 ${\displaystyle n}$ 波長（nm） 2 3 4 5 6 7 8 9 10 11 ${\displaystyle \infty }$ 121.6 102.5 97.2 94.9 93.7 93 92.6 92.3 92.1 91.9 91.15

解釋和推導

${\displaystyle E_{n}=-{{me^{4}} \over {2\left(4\pi \varepsilon _{0}\hbar \right)^{2}}}{1 \over n^{2}}=-{13.6 \over n^{2}}[{\mbox{eV}}].}$

${\displaystyle \lambda ={{hc} \over {E_{i}-E_{f}}}.}$

${\displaystyle \lambda ={12430 \over {E_{i}-E_{f}}}.}$

${\displaystyle {1 \over \lambda }={{E_{i}-E_{f}} \over 12430}=\left({12430 \over 13.6}\right)^{-1}\left({1 \over m^{2}}-{1 \over n^{2}}\right)=R\left({1 \over m^{2}}-{1 \over n^{2}}\right)}$

${\displaystyle {1 \over \lambda }=R\left({1 \over 1^{2}}-{1 \over n^{2}}\right)}$