Question

Using the Bohr model, determine the electric current produced by the electron if the hydrogen atom is in the ground state.
$\begin{aligned} & A.2.14\times {{10}^{-35}}A \\\ & B.4.48\times {{10}^{-30}}A \\\ & A.24\times {{10}^{-30}}A \\\ & A.70\times {{10}^{-35}}A \\\ \end{aligned}$

Answer 1

The number of revolutions per unit time has to be found first. Using this the current is to be calculated. This will be found by taking the product of the charge of the electron in the orbit of the hydrogen atom and the number of revolutions it undergoes per unit time. This will help you in answering the question.

Complete step by step answer:
The number of revolutions occurring per unit time is to be calculated first. This will be found using the equation which is given as,
$n=\dfrac{2\pi {{a}_{0}}}{v}$
Where ${{a}_{0}}$ be the radius of the Bohr orbit and $v$ be the velocity of the wave in motion. The number of revolutions is obtained by taking the ratio of the wavelength of the wave which will be equivalent to the circumference of the orbital to the velocity of the wave.
Now let us find out the current created in the orbit. It can be mentioned in the form of equation as,
$i=e\times \dfrac{2\pi {{a}_{0}}}{v}$
As we all know,
The radius of the first orbit of the hydrogen atom is given as,
${{a}_{0}}=0.529\overset{0}{\mathop{A}}\,=0.529\times {{10}^{-10}}m$
The velocity of the wave in the first orbit can be written as,
$v=2.19\times {{10}^{6}}m{{s}^{-1}}$
And the charge of the electron can be written as,
$e=1.69\times {{10}^{-19}}C$
Substituting the values in the equation will give,
$i=1.69\times {{10}^{-19}}\times \dfrac{2\pi \times 0.529\times {{10}^{-10}}}{2.19\times {{10}^{6}}}$
The equation can be simplified as,
$i\approx 2.14\times {{10}^{-35}}A$

So, the correct answer is “Option A”.

Note: The current is found by taking the ratio of the charge flowing to the time taken for the flow. The time taken will be the time period of the wave. And the time period is the reciprocal of the number of revolutions per unit time of the wave. The charge flowing will be one unit charge as the hydrogen atom contains only one electron.