Experimentally it is found that 12 . 8eV energy is required to...

The given data is

$q = 1 . 6 \times {10}^{- 19}C\dfrac{1}{4{\pi ε}_{0}} = 9 \times {10}^{9}N{m}^{2}{C}^{- 2}$

The formula for the value of energy in a hydrogen atom is given by

$E = \dfrac{{q}^{2}}{8\pi{ε}_{0}r} ⇒ E = \dfrac{{q}^{2}}{2 ( 4\pi{ε}_{0} ) r}$

$⇒ r = \dfrac{9 \times {10}^{9} \times 1 . 6 \times {10}^{- 19}}{12 . 8 \times 2}$

$⇒ r = \dfrac{9}{16} \times {10}^{- 10}m$

It is given that $r = \dfrac{9}{x} \times {10}^{- 10}m ⇒ \dfrac{9}{16} \times {10}^{- 10} = \dfrac{9}{x} \times {10}^{- 10} ⇒ x = 16$