The ground state energy of hydrogen atom is $\displaystyle -13 \cdot 6 \mathrm{eV}$ in Bohr model. An electron makes a transition from an energy level of -$\displaystyle 1.51$ eV to that of $\displaystyle -3 \cdot 4 \mathrm{eV}$. Calculate the wavelength of the spectral line emitted.

\[\begin{aligned} \Delta E & =E_{2}-E_{1} \\ & =(-1.51-(-3.4)) \mathrm{eV} \end{aligned} \] \[\begin{aligned} & =1.89 \mathrm{eV} \\ & =1.89 \times 1.6 \times 10^{-19} \mathrm{~J} \\ & \begin{aligned} \Delta E & =\frac{h c}{\lambda} \\ \lambda=\frac{h c}{\Delta E} & =\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{1.89 \times 1.6 \times 10^{-19}} \mathrm{~m} \\ & =6.58 \times 10^{-7} \mathrm{~m} \\ & =658 \mathrm{~nm} \end{aligned} \end{aligned} \]