While in principle we could attempt to solve for the exact equations that correspond to the energy levels of

different substances, this is extremely complicated. However, it is often simpler to determine these energy

levels experimentally. We can excite a gas electrically so that the electrons in the various orbitals will jump

up to a higher energy state, and thus regularly decay to lower energy states, thereby emitting photons as

above. If the energy levels are quantized, then we will see a discrete set of colors, which generally combine

to form a single color. We can then use a diffraction grating to separate these colors; they diffract at different

angles based on their wavelength according to Eq$.(6\mathrm{.}1),$ and it is then simple to measure these angles.

We can test our understanding of this by using the grating spectrometer to study the spectral lines of hydro$-$

gen, to reproduce the known $($both theoretically and empirically$)$ spectrum. Additionally, we can calibrate

the equipment $($i$.$e$.,$ determine the grating spacing $d)$ with the known spectrum of mercury. Finally we will

use this to determine the composition of an unknown sample. This technique $($and a variation of it$)$ is quite

important in astrophysics, to determine the composition of different gases of stars.

Looking at the table on page $53,$ explain why when to use the mercury spectrum as opposed to the

hydrogen spectrum to determine the grating spacing $d?$