Question

$2g$ of hydrogen atoms are excited to radiation. The study of spectra indicated $25\%$ of atoms are in $II{I}^{rd}$ energy level and $20\%$ atoms in $I{I}^{nd}$ energy level and rest in ground state. Calculate the total energy evolved when atoms return to ground state.

Answer 1

• Mass of H-atoms in $II{I}^{rd}$ level $=\frac{25}{100}\times 2g=0.5g$
  
• Number of moles of H-atom in $II{I}^{rd}$ level $=\frac{0.5}{1}=0.5$
• Number of atoms in $II{I}^{rd}$ level $=0.5\times 6.02\times {10}^{23}=3.01\times {10}^{23}atoms$
• Mass of H-atoms in $I{I}^{nd}$ level $=\frac{20}{100}\times 2g=0.4g$
• Number of moles of H-atom $=\frac{0.4}{1}=0.4$
• Number of atoms in $I{I}^{nd}$ level $=0.4\times 6.02\times {10}^{23}=2.408\times {10}^{23}atoms$
• Energy evolved on returning from $II{I}^{rd}$ level to ground state

$E_3-E_1=13.6(1-\frac{1}{3^2})\times 3.01\times {10}^{23}=36.4\times {10}^{23}eV$

• Energy evolved in transition from $I{I}^{nd}$ level to round state

$E_2-E_1=13.6(1-\frac{1}{2^2})\times 2.408\times {10}^{23}=24.6\times {10}^{23}eV$

• Total energy evolved $=(36.4\times {10}^{23})+(24.6\times {10}^{23})eV$

$=61\times {10}^{23}eV$

$=61\times {10}^{23}\times 1.6\times {10}^{-19}J$

$=976kJ$