# Beam width uncertainty, deflection

1. Jun 10, 2013

### unscientific

1. The problem statement, all variables and given/known data

In a scanning electron microscope, a 0.3 keV electron beam, collimated by an
aperture of width ∆xi, is directed towards a target 1 m away from the aperture. Assuming a ﬁeld-free region from aperture to target, the uncertainty ∆xf in the transverse
coordinate of the electron when it hits the target comes in part from the uncertainty
in the initial coordinate and in part from the uncertainty in the transverse velocity
∆vx. What is the typical distance by which the electrons miss the target, given that
the beam is aiming with the highest possible precision? Find the value of ∆xi that
gives the smallest total uncertainty ∆xf. Discuss quantitatively whether your result is
in accordance with electron diﬀraction of a slit of width ∆xi
. [10]
You now enter a contest in which the contestants drop a marble with a mass of
20 g from a tower onto a small target 25 m below. As for the electrons, ﬁnd the value
of the uncertainty ∆xi in the initial transverse coordinate that gives the smallest total
uncertainty ∆xf at the ground. Comment on the relevance of your result. [5]

I'm not sure if I'm interpreting the question correctly..

2. Relevant equations

3. The attempt at a solution