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In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius $5 \times 10^{-11} \mathrm{~m}$, at a speed $2.2 \times 10^{6} \mathrm{~m} / \mathrm{s}$. What is the current associated with electron motion?
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Verified Answer
The correct answer is:
$1.12 \mathrm{~mA}$
Frequency of revolution of electron,
$$
\mathrm{f}=\frac{\mathrm{v}}{2 \pi \mathrm{r}}=\frac{2.2 \times 10^{6}}{2 \pi\left(5 \times 10^{-11}\right)}=7.0 \times 10^{15} \mathrm{~Hz}
$$
Current associated, $\mathrm{i}=\mathrm{qf}$
$$
\begin{aligned}
&=\left(1.6 \times 10^{-19}\right)\left(7.0 \times 10^{15}\right) \\
&=11.2 \times 10^{-4} \mathrm{~A}=1.12 \mathrm{~mA}
\end{aligned}
$$
$$
\mathrm{f}=\frac{\mathrm{v}}{2 \pi \mathrm{r}}=\frac{2.2 \times 10^{6}}{2 \pi\left(5 \times 10^{-11}\right)}=7.0 \times 10^{15} \mathrm{~Hz}
$$
Current associated, $\mathrm{i}=\mathrm{qf}$
$$
\begin{aligned}
&=\left(1.6 \times 10^{-19}\right)\left(7.0 \times 10^{15}\right) \\
&=11.2 \times 10^{-4} \mathrm{~A}=1.12 \mathrm{~mA}
\end{aligned}
$$
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