In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5\AA$. If the speed of electron is $2.2\times 10^{6}\mathrm{~m}/\mathrm{s}$, then the current associated with the electron will be $\simeq$ ______ $\times 10^{-2}\mathrm{~mA}$. [Take $\pi$ as $\frac{22}{7}$]

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Modern Physics

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius

0.5 \overset{˚}{A}

. If the speed of electron is

2.2 \times 1 0^{6} m / s

, then the current associated with the electron will be

≃

______

\times 1 0^{- 2} mA

. [Take

π

\frac{22}{7}

]

Answer: 112

Solution

The orbiting electron carries its charge past any point of the orbit once per revolution, so the equivalent current is

I = \frac{e}{T}

with

T = \frac{2 π r}{v}

T = \frac{2 \times \frac{22}{7} \times 0.5 \times 1 0 ^{- 10}}{2.2 \times 1 0 ^{6}} = 1.43 \times 1 0^{- 16} s

I = \frac{1.6 \times 1 0 ^{- 19}}{1.43 \times 1 0 ^{- 16}} = 1.12 \times 1 0^{- 3} A = 1.12 mA

Measured in units of

1 0^{- 2}

mA, the current is

112

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Integer answer

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