An electron has an uncertainty in its position of 584pm. What is the uncertainty in its velocity?

Question

Express your answer with the appropriate units.

Answer 1

The Heisenberg Uncertainty Principle states that:

dX*dP >= h/2

where dX is uncertainty in position, dP is uncertainty in momentum, and h is Planck's constant.

You can calculate dP from this principle by plugging in dX of (5.84 * 10^-12 m) giving a momentum that is 5.67294521*10^-23 kg*m/s. You can take the momentum and relate it to mass and velocity:

dP = m*dV

where m is electron mass (9.109*10^-31 kg) in this case and dV is the uncertainty in the velocity. Dividing dP/m you get an answer of 62278463.17 m/s.