## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

When $n = 6$: $\lambda = 410.06~nm$ When $n = 8$: $\lambda = 388.80~nm$ When $n = 10$: $\lambda = 379.69~nm$
We can use the following equation to find the wavelengths of spectral lines in the Balmer series: $\frac{1}{\lambda} = R~(\frac{1}{2^2}- \frac{1}{n^2})$ Note that $R$ is the Rydberg constant and $R = 1.0974\times 10^7~m^{-1}$ When $n = 6$: $\frac{1}{\lambda} = R~(\frac{1}{2^2}- \frac{1}{n^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{1}{2^2}- \frac{1}{6^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{2}{9})$ $\frac{1}{\lambda} = 0.24387\times 10^7~m^{-1}$ $\lambda = 4.1006\times 10^{-7}~m$ $\lambda = 410.06~nm$ When $n = 8$: $\frac{1}{\lambda} = R~(\frac{1}{2^2}- \frac{1}{n^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{1}{2^2}- \frac{1}{8^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{15}{64})$ $\frac{1}{\lambda} = 0.2572\times 10^7~m^{-1}$ $\lambda = 3.8880\times 10^{-7}~m$ $\lambda = 388.80~nm$ When $n = 10$: $\frac{1}{\lambda} = R~(\frac{1}{2^2}- \frac{1}{n^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{1}{2^2}- \frac{1}{10^2})$ $\frac{1}{\lambda} = (1.0974\times 10^7~m^{-1})~(\frac{6}{25})$ $\frac{1}{\lambda} = 0.263376\times 10^7~m^{-1}$ $\lambda = 3.7969\times 10^{-7}~m$ $\lambda = 379.69~nm$