Calculate the uncertainty in position of an electron that has been accelerated across a potential difference of 100 kV +/- 100 V.
Hints: Derive an expression for the momentum as a function of the voltage (potential difference) and differentiate. Also dV may be represented by the uncertainty in the voltage (i.e. +/- 100 volts = 200 V)
Relationship between kinetic energy and voltage : E_k = V*q© BrainMass Inc. brainmass.com March 4, 2021, 6:09 pm ad1c9bdddf
As per given problem,
Ek = V * q = 100kV * 1 = p2 / 2m,
where, m is the mass of electron and q = as one ...
This solution includes four steps of calculations. Uncertainty in position can be found by putting the values of m, V , h and dV in the resulting expression.