A microscope using photon to locate an electron in an atom to within a distance of 0.2A,what is the uncertainty in the moment of the electron measured in this way?

1 Answer
Apr 17, 2018

See below

Explanation:

You either locate the electron or you don't.

There is a strict mathematical limitation which says that:

#sigma_x sigma_p ge h/(4 pi)#

But this does not mean that you can choose to locate the electron within a range and be guaranteed a range of momenta.

Instead, if you conducted the same experiment a billions times and discovered that the standard deviation in the position of the electron was 0.2 A, you would be guaranteed, were you to begin measuring momentum instead, that the standard deviation in your momentum measurements would be at least:

  • #h/(4 pi) * 1/( 0.2 * 10^(-10))#