Question

A Transmission Electron Microscope (TEM) is a kind of electron microscope that images by detecting electrons that pass through a sample (hence, the tranmission). This requires both very thin samples and much higher electron kinetic energies, at least an order of magnitude greater than a conventional Scanning Electron Microscope (SEM). If a particular TEM operates with an accelerating voltage of 150 kV, and therefore electrons with kinetic energies of 150 keV (recall KE = q∆V ), calculate the theoretical smallest size object this TEM can resolve.

Answer 1

Here the given details : Electrons with kinetic energy, E= 150keV=150*103 eV.

Let the smallest size of object that can resolve is d.

The required formula to find d (resolution of TEM microscope) is given by Abbe's equation:

where,

= electrons wavelength

n= refractive index

= maximum half angle

NA = = numerical aperture of the microscope.

Now taking into account the relativistic effects, the electron wavelength become,

where,

h = planck's constant = 6.626*10-34 J.s

mo = rest mass of electron = 9.1*10-31 kg

Now here in the qustion, no details about the numerical apperture is given. So I take the value of NA is euals to 0.87 for = and n = 1.

now for the given values,

= 1.325*10-30 meter.

And the smallest size(resolution) of the object that can be detected is d = 7.61*10-31 meter = 7.61*10-19 picometer.