00:01
So let's say we're trying to image an atom, which has a diameter, i know this is a very crude drawing, of about 100 picometers or so, and we need to resolve to a width, we'll call our resolution, i guess, delta x, i suppose, of 10 picometers.
00:21
And so for references, 10 to the negative 11th meters, because a picometer is 10 to the negative 12th.
00:28
So if we use an electron microscope, what energy do we need for our electrons? so basically we want our wavelength to be equal to this resolution distance.
00:39
And so this is going to be planks constant divided by the momentum.
00:43
And we know the momentum is like a square root of two times the mass of the electron times the energy of the electron.
00:50
So if we rearrange this, what we'll have is the square root of 2m times e equals planks constant divided by delta x.
00:59
So if we square both sides, we'll get 2me equals h squared over delta x squared.
01:07
And so the energy that we're looking for for our particular electron is h bar squared over 2m delta x squared, kind of reminiscent of maybe your particle in a box energy levels.
01:20
So if we plug in our values, this is 6 .63 times 10 to the negative 34th joules squared...