# Sorry for naive question: Does a single electron have an atto or femto-amperage?

Single electron counters appear to exist, the Jap. have one that even determines direction, and they discuss atto-amperage. What I don't quite get is, if a single electron flows, is there an observed very small current ? Since an electron is the smallest size, more sensitive equipment then can never discover an even smaller current, right ?

I accept the notion that models may call for a smallest indivisible unit, I'm only wondering how we establish that we have indeed located that size. Thanks for commenting..

## Answers and Replies

If the particle undergoes a finite and quasiperiodic motion, then the electric current could be quantified as the charge of the particle divided by the period. For example, for the hydrogen atom:

$$\left\{\begin{array}{lcl} \frac{m_{e} v^{2}}{r} & = & \frac{k_{0} e^{2}}{r^{2}} \\ m_{e} v r & = & \hbar \end{array}\right. \Rightarrow \left\{\begin{array}{lcl} v^{2} r & = & \frac{k_{0} e^{2}}{m_{e}} \\ v r & = & \frac{\hbar}{m_{e}} \end{array}\right.$$

$$\left\{\begin{array}{lcl} v & = & \frac{k_{0} e^{2}}{\hbar} \\ r & = & \frac{\hbar^{2}}{m_{e} k_{0} e^{2}} \end{array}\right.$$

The period is:

$$T = \frac{2 \pi r}{v} = \frac{1}{4 \pi^{2} c} \frac{(h c)^{3}}{m_{e} c^{2} (k_{0} e^{2})^2} = 1.520 \times 10^{-16} \, \mathrm{s}$$

This gives a current of:

$$I = \frac{e}{T} = 1.05 \, \mathrm{mA}$$

thx for formula, could you also paste the terms, definitions ? Also the last term is not clear to me,i.e. the 1.05 mA (!). I'm not in physics, would appreciate discussion of hardware level, if any. I read the wikipedia articles, they did not really center on measurement and instrument sensitivity.

No, I can't. Look for Bohr model lectures. $mA$ stands for 'milliampere'. Learn the prefixes for SI units.

What I don't quite get is, if a single electron flows, is there an observed very small current ?

Current density can be seen as the product of the number of charges and their drift speed:
http://en.wikipedia.org/wiki/Current_density

So according to the first equation in that link, nothing prevents having a single electron going at arbitrary low speed, from which you can easily get an atto-ampere if you want. Current depends on both the number of charges and their drift velocity (itself a function of resistance and voltage in paticular).