Question

Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length $1\times {10}^{-10}m$.

Answer 1

This is a simple application of Heisenberg’s uncertainty principle, which is as follows:

$\Delta x\Delta p\ge \frac{h}{4\pi }$

where $\Delta x$ is the uncertainty in position, and $\Delta p$ 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,

$\Delta p\ge$$\frac{h}{4\pi \Delta x}$

$\Delta p\ge \frac{6.62607004\times {10}^{-34}}{4\pi \times {10}^{-10}}$

Which means your Uncertainty in Momentum is approximately,

Therefore ;

$5.27286\times {10}^{-25}{kgms}^{-1}$