Calculate the speed of an electron in the ground state of ${\mathrm{He}}^{+}$ ion. What fraction of speed of light is this value? How long does it take for the electron to complete one revolution around the nucleus. How many times does the electron travel around the nucleus in one second?

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 ${\mathrm{a}}_0$.

${\mathrm{S}}_1 :$ Bohr model is applicable for ${\mathrm{Be}}^{2+}$ ion.
${\mathrm{S}}_2 :$ Total energy coming out of any light source is an integral multiple of the energy of one photon.
${\mathrm{S}}_3 :$ Number of waves present in the unit length is the wave number.

${\mathrm{S}}_4 : \mathrm{e}/\mathrm{m}$ ratio in cathode ray experiment is independent of the nature of the gas.