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  • 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  <

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}\times10^{-10}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 \text { and electronic charge }=1.6 \times 10^{-19} \mathrm{C}\right)

Option: 1

16


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Using total energy= E=\frac{ke^{2}}{2r}

r=\frac{ke^{2}}{2E}

Given E = 12.8 eV = 12.8 × e Joule

\begin{aligned} & r=\frac{9 \times 10^9 \mathrm{e}^2}{2 \times 12.8 \mathrm{e}}=\frac{9 \times 10^9 \times 1.6 \times 10^{-19}}{2 \times 12.8} \\ & r=\frac{9 \times 10^{-10}}{(2 \times 12.8 / 1.6)}=\frac{9 \times 10^{-10}}{16} \mathrm{~m} \end{aligned}

Therefore x = 16

 

Posted by

Devendra Khairwa

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