Symbols in Heisenberg's Uncertainty Principle

Question

The uncertainty principle states that $${\Delta}x{\Delta}p{\geq}\frac{h}{4\pi}.$$

In experimental uncertainty, ${\Delta}x$ is actually half the range (since the value implies that the actual value might be ${\Delta}x$ greater or ${\Delta}x$ less).

In this equation, is ${\Delta}x$ (or ${\Delta}p$) given by the range, or half the range just like experimental uncertainties? Specifically, in a hydrogen atom, is ${\Delta}x$ of the orbiting electron given by the diameter of the orbit or the radius of the orbit, and is ${\Delta}p$ given by twice its magnitude of momentum?

Answer 1

$\Delta x$ is neither the radius nor the diameter of your orbit. It is the standard deviation representing the region in which the particle could be.