The correct option is A 3.35×10−3 ms−1
We know that from Heisenberg's uncertainity principle,
Δx.Δp≥h4π
where Δx:uncertainity in position
Δp:uncertainity in momentum
h:planck's constant
Side of cube =10 mm=10×10−3 m
Maximum uncertainity in position = Length of body diagonal of cube. Because it is the maximum possible length in the cube.
∴Δx=10√3 mm=10√3×10−3 m
Here, p=mv
∴Δp=Δ(mv)
⇒ Δp=mΔv
∴Δv≥h4πmΔx
≥6.626×10−344×3.14×(9.1×10−31)×(10√3×10−3)
∴Δv≥3.34×10−3 m/s