Heisenberg Uncertainty principle in 3D

[mat8845]

Hi there,

So here's my assignment:

''The velocity of a positron is measured to be: v_x=(4.00±0.18)*10⁵ m/s, v_y=(0.34±0.12)*10⁵ m/s, v_z=(1.41±0.08)*10⁵ m/s. Within what minimum volume was the positron located at the moment the measurement was carried out?''

I think I'm not wrong when I say that the uncertainty principle applies in every direction. Since the velocities are not relativistic, the simple equation should be:

Δx=hbar/(2*m*Δv_x)

The same equation is used for Δy and Δz, and we only take the volume of the ''uncertainty box'' V=ΔxΔyΔz.

With the positron having a mass of 9.109*10^-31kg, that gives me V=1.12*10^-25 m³. But I know the right answer is 1.4*10^-26 m³.

Even with the relativistic equations, I get the same wrong answer.

So what am I doing wrong? Note that I never used the values of the velocities. Should I use them somewhere?

Thank you for your time.

 

[mat8845]

Nevermind, there was a mistake in the book.