Experimentally it is found that 12.8 ,eV energy is required to se… - Vidyadip

MCQ

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 $\left(1\,eV =1.6 \times 10^{-19}\,J , \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\,Nm ^2 / C ^2\right.$ and electronic charge $=1.6 \times 10^{-19}\,J\,C$ )

A
$15$
B
$14$
✓
$16$
D
$13$

✓

Answer

Correct option: C.

$16$

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

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

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

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

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