Solutions to Exercises Heisenberg Principle

Solutions/Answers to Exercises

Exercise 1. Calculate the uncertainty in the position of a proton moving at a speed of (2.80 ± 0.01) x 104 m/s.


The uncertainty in the speed is 0.01 x (2.80 x 104 m/s) = 2.80 x 102 m/s.
The mass of a proton, in kg, is 1.67 x 10-27 kg.

\(\displaystyle \Delta x\;\geq\;\frac{h}{4\pi m\Delta\nu}\;=\;\frac{6.626\times\;10^{-34}\frac{kg⋅s^2}{m^2}⋅s}{4\pi(1.67\
times\;10^{-27}\;kg\times\;(2.80\times\;10^2\;m/s))}=\mathbf{1.13\times\;10^{-10}\;m}\)


Exercise 2. Calculate the uncertainty in the position of a neutron moving at a speed of (1.80 ± 0.01) x 105 m/s.

The uncertainty in the speed is 0.01 x (1.80 x 104 m/s) = 1.80 x 102 m/s.
The mass of a neutron, in kg, is 1.67 x 10-27 kg.

\(\displaystyle \Delta x\;\geq\;\frac{h}{4\pi m\Delta\nu}\;=\;\frac{6.626\times\;10^{-34}\frac{kg⋅s^2}{m^2}⋅s}{4\pi(1.67\
times\;10^{-27}\;kg\times\;(1.80\times\;10^2\;m/s))}=\mathbf{1.75\times\;10^{-10}\;m}\)

Back to Heisenberg Uncertainty Principal

Leave a Reply

Your email address will not be published. Required fields are marked *