How Does Optical Radiation Affect Electron Velocity Uncertainty?

[clambake]

Homework Statement

Suppose optical radiation (gamma = 5.00 x 10^-7 m) is used to determine the position of an electron to within the wavelength of the light. What will be the resulting uncertainty in the electron's velocity?

wavelength = 5.00 x 10^ -7 m
mass of electron = 9.11 x 10^ -31 kg

Homework Equations

gamma = h/p = h/mv
(delta x)(delta p) = h/4pi

The Attempt at a Solution

I solved for momentum and got 1.33 x 10^-27 kg. I tried to then plug that value back into the equation and solve for velocity, but the answer is way off. I am sure I need to use the uncertainty principle equation, but I'm not sure where to go. I can solve for delta x, and then...?

 

[alphysicist]

Hi clambake,

You do need to use the uncertaintly principle equation. They want the uncertainty in the electron's velocity, so you need to use the equation to find the uncertainty in the momentum (delta p).

To get that, you first need the uncertainty in the position (delta x). That (delta x) will depend upon how the measurement is being made. What does the problem statement say about the measurement uncertainty?