The reaction between ${\mathrm{H}}_2$ and ${\mathrm{Br}}_2$ to form $\mathrm{HBr}$ in presence of light is initiated by the photo decomposition of ${\mathrm{Br}}_2$ into free $\mathrm{Br}$ atoms (free radicals) by absorption of light. The bond dissociation energy of ${\mathrm{Br}}_2$ is $192 \mathrm{kJ}/\mathrm{mole}.$ If the longest wavelength of the photon that would initiate the reaction is $\mathrm{y}\stackrel{\circ }{\mathrm{A}}.$ Then find value of $\mathrm{y}.$

Use: Planck's constant$=6.62\times {10}^{-34}\mathrm{Js}$ and Avogadro's number $=6.02\times {10}^{23}$

The quantum yield for decomposition of $\mathrm{HI}$ is $0.2.$ In an experiment $0.01$ moles of HI are decomposed. If the number of photons absorbed is $3\times {10}^{\mathrm{x}}.$ Then find value of $\mathrm{x}.$

Use : Avogadro's number $6.02\times {10}^{23}$

The ionisation energy of a H-like Bohr atom is $4$ Rydbergs.

(i) What is the wavelength of radiation emitted when the ${\mathrm{e}}^{-}$jumps from the first excited state to the ground state?

(ii) What is the radius of first Bohr orbit for this atom? [$1$ Rydberg $\left.=2.18\times {10}^{-18} \mathrm{J}\right]$

Photon having wavelength $12.4 \mathrm{nm}$ was allowed to strike a metal plate having work function $25\mathrm{eV}$. Calculate the -

(a) Maximum kinetic energy of photoelectrons emitted in $\mathrm{eV}$.

(b) Wavelength of electron with maximum kinetic energy in $\mathrm{\AA }$.

(c) Calculate the uncertainty in wavelength of emitted electron, if the uncertainty in the momentum is $6.62\times {10}^{-28} \mathrm{kg} \mathrm{m}/\sec$