# What is currently the approximate precision or accuracy $\delta r$ with which the position $r$ of an electron can be measured?

The measurement of the position of an electron has associated, on the one hand, a quantum uncertainty $\Delta r$ which gives an idea of the probability cloud where the electron can appear, for example it gives the idea of orbital in the case of an electron bound to an atom; and of course $\Delta r$ has nothing to do with our technology. To get information about the probability clouds scientists often work both mathematically and experimentally with a lot of electrons treated statistically (distribution measurements, massive diffraction in crystals, etc).

On the other hand, and that's the topic I want to address, let's suppose the measurement of the position of a single electron, whether bound or free; it has associated a precision or accuracy or error $\delta r$ around the measured position $r$, which is entirely due to the apparatus or to our technological development.

In a former bad-posed question I didn't realize I was confusing these two uncertainties, $\Delta r$ and $\delta r$; thanks to @EmilioPisanty for the comments about that. So I open this new supposedly-well-posed-question.

What is curious is that we always find papers and experiments where they talk a lot about values of measurements, distributions, uncertainties, values of $\Delta r$, clouds, plots of wave functions, shapes of packets, etc, but it's really difficult to find some actual value of the accuracy $\delta r$. How good, approximately, are our experimental devices and technology in 2010-2020 with respect to $\delta r$?

(Also, though this could belong to a new question, any information about the relationship between $\delta r$ and the uncertainty principle, e.g. if this principle is really talking about $\delta r$, $\Delta r$, or both).

• Suppose you shot a stream of electrons through an adjustable width slit. The uncertainty of the position for passing electrons (when they pass through the slit) would be the slit's width. How thin you could get the slit and still pass electrons through would, of course be related to the wavelength of the electrons, but in principle, the question you're asking depends on the conjugate variables so much that I'm not sure an answer would have any meaning. – user121330 Nov 7 '17 at 18:54
• – Emilio Pisanty Nov 7 '17 at 19:19
• @user121330: Yes, the idea of the electron passing undeviated through a very thin slit (e.g. between two close atoms in a foil) could give a first upper bound of the order of magnitude of this δr (which anyway seems to be an unimportant magnitude, see below). – Victor Graus Nov 13 '17 at 16:24