If the work function $\left(\mathrm{w}\right)$ of an arbitrary metal is $3.1 \mathrm{eV}$, find its threshold wavelength and the maximum kinetic energy of the electron emitted when the radiation of $300 \mathrm{nm}$ strikes the metal surface. (Take $\mathrm{hc}=12400 \mathrm{eV} \stackrel{\circ }{\mathrm{A}}$).

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 $436 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{S}}_1 :$ 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.