Quiz

Well, half a millimeter, if going deeper, and if the deepest point is the middle of the capacitor.

Yes, the answer is correct. It's just that, terminologically, you can't go deeper into a one-millimeter object than half a millimeter. After going half a millimeter deep, the electron will start moving towards the opposite surface.)
A more obvious riddle: "How deep into the forest can a deer run?"
Hermit, please, ask the next riddle.

The force that will slow down the electron: F = 3.8 * 10-6 * 1.6 * 10-19 = 6.08 * 10-25 N
The deceleration will be: a = F/m = 6.08 * 10-25 / 9 * 10-31 = (6.08/9) * 106 m/s2
And then we'll calculate the distance: s = v2 / (2a) = 1002 / (2 * (6.08/9) * 106) = 104 / (106 * 2 * 6.08/9) = 9 / (100 * 2 * 6.08) = 9 / 1216 = 0.0074013157895 m

By the way, I chose the numbers so that the result would be 0.75 mm if you start solving such a problem. I must have made a mistake by an order of magnitude somewhere, I was calculating "in my head." Never mind, it doesn't matter for the solution; the numbers are symbolic.