Question about the uncertainty principle?

[zeromodz]

Okay I actually have 2 questions.

1)

ΔxΔp >= h / 2π

Is x one dimensional? Say if I wanted to locate the certainty of an electron in a hydrogen atom with a diameter of 10e-10 m. The electron is confined to the volume of the atom, not just the diameter, so could I say

Δx = 10e-10
or
Δx = (4/3)(π)(10e-10 / 2)^3

Is x in units of length or volume?

2) Say if I calculate an uncertainty of

Δx >= 12

That means I can assume that x can be anywhere greater than or equal to 12, right?

That expresses that I know for certain that x < 12. I just want to make sure I understand this whole uncertainty thing. Thanks

 

[Matterwave]

2)
x is one dimensional and has units of length (Planck's constant has units of angular momentum, so it's the same units and length times momentum). The uncertainty principle only applies to non-commuting operators, therefore, since the only momentum that x does not commute with is the momentum in the x-direction (it commutes with the momentum in the y, and z directions), there is only an "uncertainty" in x and px, y and py, and z and pz, but there is no uncertainty in say x and py, or z and px.

I'm not sure I can explain that better haha, sorry.

2) Uncertainty being greater than 12 just means you can't know x to a higher degree of accuracy than 12 (in units w/e). It doesn't mean x is confined to be outside 12 though, you just can't confine it for certain within 12.