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 . The value of the is [2023]

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Solution

Q.
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 $\frac{9}{x} \times 10^{- 10} m$ . The value of the $x$ is _________.

$(1 eV = 1.6 \times 10^{- 19} J, \frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2}$ and electronic charge $= 1.6 \times 10^{- 19} J C)$ [2023]

Ans.
(16)

$Binding energy of system = \frac{k e^{2}}{2 r} joule and \frac{k e^{2}}{2 r} = 12.8 eV$

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

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

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

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