Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length 1×10−10m.
This is a simple application of Heisenberg’s uncertainty principle, which is as follows:
ΔxΔp≥h4π
where Δx is the uncertainty in position, and Δp is the uncertainty in momentum and h is the planks constant.
Now, the uncertainty in a position here is simply the region where your electron is confined.
Here it is 10−10
Therefore,
Δp≥h4πΔx
Δp≥6.62607004×10−344π×10−10
Which means your Uncertainty in Momentum is approximately,
Therefore ;
5.27286×10−25kgms−1