# Can we find 100% probability region in an orbital if the position of an electron is limited by speed of light?

The square of the wavefunction gives probability density of finding an electron somewhere in the orbital.

The text I'm referring to says that the value of probability density is always higher than zero at any finite distance from the nucleus.

My question is, provided that we knew position of an electron at a give time, could we now draw a boundary surface diagram that encloses a region in which probability of finding the electron is 100% for some point in time in future?

This would be possible because the electron cannot travel faster than the speed of light, so we could draw a sphere of radius $3*10^8$ meters centered at the current known position and say that probability of finding the electron after one second will not be beyond the region enclosed by the sphere.

Or is this question invalid because we can't know the position of an electron ever, not even within a finite uncertainty that would allow us to draw such a sphere?

• Your own objection to your idea is right: we can never know the position of an electron. – Ivan Neretin Mar 29 '16 at 11:02
• @IvanNeretin is it because of Hiesenberg's uncertainty principle? (shouldn't that still allow for knowledge of position within a finite uncertainty)? – Peeyush Kushwaha Mar 29 '16 at 11:22
• Well, yes, we might put it this way. Finite uncertainty of position does not imply finite distance. Look again at that Gaussian bell curve (or just about any other probability distribution, for that matter): it surely has finite uncertainty, but it continues to infinity and never quite reaches 0. – Ivan Neretin Mar 29 '16 at 11:33
• @IvanNeretin I think I got it now. I always thought that uncertainty principle related $\Delta x$ and $\Delta p$ where these give a range of values that velocity or position may take (i.e. x will lie with 100% probability between $x - \Delta x$ and $x + \Delta x$ ) but actually it relates $\sigma_x$ and $\sigma_p$ where these are the standard deviations in the probability distribution. Am I correct? – Peeyush Kushwaha Mar 31 '16 at 6:53
• That's right, these are the standard deviations. There is no 100% probability interval. – Ivan Neretin Mar 31 '16 at 7:17