Why is the cathode ray tube experiment not conducted at atmospheric pressure?

The energy levels of hypothetical one electron atom are shown below.
$0 \mathrm{eV\_\_\_\_\_n}=\infty$
$-0.50 \mathrm{eV\_\_\_\_\_n}=5$
$-1.45 \mathrm{eV\_\_\_\_\_n}=4$
$-3.08 \mathrm{eV\_\_\_\_\_n}=3$
$-5.3 \mathrm{eV\_\_\_\_\_n}=2$
$-15.6 \mathrm{eV\_\_\_\_\_n}=1$
$\left(\mathrm{a}\right)$ Find the ionisation potential of atom?
$\left(\mathrm{b}\right)$ Find the short wavelength limit of the series terminating at $\mathrm{n}=2$?
$\left(\mathrm{c}\right)$ Find the wave number of photon emitted for the transition made by the electron from third orbit to first orbit?
 

Calculate the energy required to excite one litre of hydrogen gas at $1 \mathrm{atm}$ and $298 \mathrm{K}$ to the first excited state of atomic hydrogen. The energy for the dissociation of $\mathrm{H}-\mathrm{H}$ bond is $436 \mathrm{kJ} {\mathrm{mol}}^{-1}$

The wave function of $3\mathrm{s}$ electron is given by  ${\mathrm{\psi }}_{3\mathrm{s}}=\frac{1}{81\sqrt{3}\mathrm{\pi }}{\left(\frac{1}{{\mathrm{a}}_0}\right)}^{3/2}\left[27-18\left(\frac{\mathrm{r}}{{\mathrm{a}}_0}\right)+2{\left(\frac{\mathrm{r}}{{\mathrm{a}}_0}\right)}^2\right]{\mathrm{e}}^{-\mathrm{r}/3{\mathrm{a}}_0}$

It has a node at $\mathrm{r}={\mathrm{r}}_0$. Find the relations between ${\mathrm{r}}_0$ and ${\mathrm{a}}_0$.