How certain do we have to get about a particle's position ?

[B4ssHunter]

i was reading brian cox's book about *the quantum universe *
and he said something interesting
if for instance we know that a particle exists in ΔX , then this delta has to be less than one wavelength * he did it with clocks * to know the probability of its existence somewhere else in the universe , because if it was more than one wavelength , probabilities would cancel each other out at this point that i want to know the probability of the existence of the particle at
but i think it would make more sense if it was actually less than HALF a wavelength , because if my certainty in the position of the particle was less than half a wavelengths , then there is going to be no chance that probabilities will cancel out , right ?

 

[HallsofIvy]

The basic formula is "(\Delta x)(\Delta p)= h) where \Delta x is the uncertainty in the position, \Delta p is the uncertainty in the momentum and "h" is "Plank's constant", about 6.26\times 10^{-34} "Joule seconds".