Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given for example, Hydrogen electron in ground state. What is probability to find that electron at certain distance (not interval of distances) from center of nucleus, for example at radial coordinate $r=0.5 \cdot 10^{-10}$ (and any angle)?

share|cite|improve this question
are you asking for the probability for an exact radius and not the probability density for that radius? – Jim Jun 24 '13 at 20:09
If so, the probability is identically zero – Jim Jun 24 '13 at 20:12
In the interests of reducing the side chatter I'll concede the infinitesimal thing and delete my comments on the matter. Thanks to joshphysics, Jim and AlfredCentauri for correcting me. – dmckee Jun 24 '13 at 23:26
up vote 1 down vote accepted

The probability of finding the particle exactly at a particular radial coordinate is zero whilst the probability of finding the particle in the infinitesimal neighborhood of that coordinate is infinitesimal.

$\int_r^r \rho(\tau)d\tau = 0$

$\int_r^{r + dr} \rho(\tau)d\tau = \rho(r)dr$

This follows from the fundamental relationship:

$f(x + dx) = f(x) + f'(x)dx$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.