Atoms And Nuclei

Experimentally it is found that \(12.8 ~\mathrm{eV}\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{x} \times 10^{-10} \mathrm{~m}\). The value of the \(x\) is __________.

\(\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right.\) and electronic charge \(\left.=1.6 \times 10^{-19} \mathrm{C}\right)\)