In Bohr’s atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 A. If the speed of electron is ${2.2×10}^{6} m / s$ , then the current associated with the electron will be ${×10}^{- 2} mA.[Take π as \frac{22}{7}]$ ___

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answer is 112.

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Detailed Solution

The current due to a unit charge e is given by,

$I = \frac{e}{T}$

In the equation, substituting

$\begin{array}{l} T = \frac{2 π}{ω} and ω = \frac{v}{r} we get, \\ I = \frac{e ω}{2 π} = \frac{e v}{2 π r} \\ I = \frac{1.6 \times 10^{- 19} \times 2.2 \times 10^{6} \times 7}{2 \times 22 \times 0.5 \times 10^{- 10}} = 1.12 mA \\ I = 112 \times 10^{- 2} mA \end{array}$