Question

The uncertainty in the position of an electron along an x axis is given as 53 pm, which is about equal to the radius of a hydrogen atom. What is the least uncertainty in any simultaneous measurement of the momentum component px of this electron?
_____ kg·m/s

Answer 1

To solve this problem it is necessary to apply the concepts related to the Heisenberg's uncertainty principle. Under this principle we understand the relationship that the minimum range of error in position (x) times the minimum range of error in momentum (p) is, at a minimum, about equal to the Planck constant, mathematically that is,

$\Delta p = \frac{h}{\Delta x}$

Replacing with our values we have,

$\Delta p = \frac{6.63*10^{-34}J\cdot s}{2\pi (53*10^{-12}m)}$

$\Delta p = 1.99*10^{-24} kg\cdot m/s$

Therefore the least uncertainty in any simultaneous measurement of the momentum component px of this electron is $1.99*10^{-24} kg\cdot m/s$