Question

In a hydrogen atom, the electron makes $6.6\times {10}^{15}\text{revolutions per second}$ around the nucleus in an orbit of radius $0.5\times {10}^{-10}\text{m}$. It is equivalent to a current nearly

• A. $1\text{A}$
• B. $1.6\times {10}^{-19}\text{A}$
• C. $1\mu \text{A}$
• D. $1\text{mA}$

Answer 1

The correct option is D $1\text{mA}$

As we know that, current is defined as

$I=\frac{q}{t}$

Here,
Charge on electron, $q=1.6\times {10}^{-19}\text{C};$
And frequency, $f=1/t=6.6\times {10}^{15}\text{Hz}$

$\therefore I=\frac{q}{t}=qf$

$\Rightarrow I=1.6\times {10}^{-19}\times 6.6\times {10}^{15}$

$\Rightarrow I=10.56\times {10}^{-4}\approx 1\text{mA}$

Hence, option $\left(b\right)$ is correct.

Why this Question ? The current at time $t$ is $$I=\underset{\Delta t\to 0}{lim}\frac{\Delta Q}{\Delta t}=\frac{dQ}{dt}$$ Thus, electric current through an area is the rate of transfer of charge from one side of the area to the another.