KCET · Physics · Current Electricity
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?
- A \(1.12 \mathrm{~mA}\)
- B \(3 \mathrm{~mA}\)
- C \(0.75 \mathrm{~mA}\)
- D \(2.25 \mathrm{~mA}\)
Answer & Solution
Correct Answer
(A) \(1.12 \mathrm{~mA}\)
Step-by-step Solution
Detailed explanation
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, \(\mathrm{i}=\mathrm{qf}\)
\(=\left(1.6 \times 10^{-19}\right)\left(7.0 \times 10^{15}\right) \)
\(=11.2 \times 10^{-4} \mathrm{~A}=1.12 \mathrm{~mA}\)
\(\mathrm{f}=\frac{\mathrm{v}}{2 \pi \mathrm{r}}=\frac{2.2 \times 10^{6}}{2 \pi\left(5 \times 10^{-11}\right)}=7.0 \times 10^{15} \mathrm{~Hz}\)
Current associated, \(\mathrm{i}=\mathrm{qf}\)
\(=\left(1.6 \times 10^{-19}\right)\left(7.0 \times 10^{15}\right) \)
\(=11.2 \times 10^{-4} \mathrm{~A}=1.12 \mathrm{~mA}\)
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