Predict/Calculate The Pickering Series In $1896,$ the American astronomer Edward C. Pickering $(1846-1919)$ discovered an unusual series of spectral lines in light from the hot star Zeta Puppis. After some time, it was determined that these lines are produced by singly ionized helium. In fact, the "Pickering series" is produced when electrons drop from higher levels to the $n=4$ level of $\mathrm{He}^{+} .$ Spectral lines in the Pickering series have wavelengths given by

$$\frac{1}{\lambda}=C\left(\frac{1}{16}-\frac{1}{n^{2}}\right).$$

In this expression, $n=5,6,7, \ldots$ (a) Do you expect the constant $C$ to be greater than, less than, or equal to the Rydberg constant $R ?$ Explain. (b) Find the numerical value of $C .$ (c) Pickering lines with $n=6,8,10, \ldots$ correspond to Balmer lines in hydrogen with $n=3,4,5, \ldots$ Verify this assertion for the $n=6$ Pickering line.