Experimentally it is found that 12.8 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 9/x x 10^-10 m. The value of the x is :________
$(1 eV = 1.6 \times 10^{- 19} J, \frac{1}{4 {πϵ}_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2}$ and electronic charge = 1.6 x 10^-19C)

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answer is 16.

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Detailed Solution

$Binding energy = \frac{1}{4 {πε}_{0}} \frac{e^{2}}{2 r} = 12.8 eV$

$9 \times 10^{9} \times \frac{{(e)}^{2}}{2 r} = 12.8 e$

$r = \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19}}{2 \times 12.8} = \frac{9}{16} \times 10^{- 10}$

$\frac{9}{16} \times 10^{- 10} = \frac{9}{x} \times 10^{- 10}$

$x = 16$

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