An electron in Bohr model of hydrogen atom makes a transition from energy level -$\displaystyle 1.51$ eV to -$\displaystyle 3.40$ eV. Calculate the change in the radius of its orbit. The radius of orbit of electron in its ground state is $\displaystyle 0.53 \AA$.

$\displaystyle E_{n}=\frac{-13.6}{n^{2}} \mathrm{~eV}$ For $\displaystyle E_{n}=-1.51 \mathrm{~eV}$: $\displaystyle -1.51=\frac{-13.6}{n^{2}}$ $\displaystyle n=3$ For $\displaystyle E_{n}=-3.40 \mathrm{~eV}$: $\displaystyle -3.40=\frac{-13.6}{n^{2}}$ $\displaystyle n=2$ $\displaystyle r=0.53 n^{2} \AA$ $\displaystyle \therefore$ change in radius: $\displaystyle \Delta r=0.53\left[3^{2}-2^{2}\right]$ $\displaystyle =0.53 \times 5$ $\displaystyle =2.65 \AA$