Question

In hydrogen atom an electron revolves in a circualr path of radius 5.0 * 10^-11 m with speed
of 2.2 * 10^6 m/s. Calculate the equivalent current. (Charge on electron e = 1.6 * 10^-19
coulomb)​

Answer 1

Given:

In hydrogen atom,

Radius of orbit, r= 5×10⁻¹¹ m

Speed of electron, v= 2.2×10⁶ m/s

Charge of electron, q= 1.6×10⁻¹⁹ C

To Find:

Equivalent current produced by electron

Solution:

We know that,

• For an electron, revolving in an orbit of an atom, equivalent current I produces by electron is given by

$\pink{\boxed{\bf{I=\frac{ev}{2\pi r}}}}$

where,

e is the charge of electron

r is the radius of orbit

v is the speed of electron

$\rule{190}{1}$

Let the equivalent current produced by electron be I

So,

$\longrightarrow\rm{I=\dfrac{ev}{2\pi r}}$

$\longrightarrow\rm{I=\dfrac{1.6\times10^{-19}\times2.2\times10^{6}}{2\times\dfrac{22}{7} \times5\times10^{-11}}}$

$\longrightarrow\rm{I=\dfrac{3.52\times10^{-13}}{\dfrac{220}{7}\times10^{-11}}}$

$\longrightarrow\rm{I=\dfrac{7\times3.52\times10^{-13}}{220\times10^{-11}}}$

$\longrightarrow\rm{I=\dfrac{24.64\times10^{-13}}{220\times10^{-11}}}$

$\longrightarrow\rm{I=0.112\times10^{-2}}$

$\longrightarrow\rm\green{I=1.12\times10^{-3}A}$

$\longrightarrow\rm\green{I=1.12\:mA}$

Hence, the equivalent current for given electron is 1.12×10⁻³A or 1.12mA.