Question #164692

caluculate the Resolution of electron microscopes and optical microscopes


1
Expert's answer
2021-02-22T10:25:18-0500

For electron microscopes:

The de Broglie wavelength associated with a particle having momentum p is given as follows.

λ=hpλ = \frac{h}{p}

Substitute K2+2KE0c\frac{\sqrt{K^2+2KE_0}}{c} for p.

λ=hK2+2KE0c=hcK2+2KE0λ = \frac{h}{\frac{\sqrt{K^2+2KE_0}}{c}} \\ = \frac{hc}{\sqrt{K^2+2KE_0}}

For a 3.0-MV transmission electron microscope:

K=3.0×106  eVE0=0.511×106  eVλ=1240  eV×nm(3.0×106  eV)2+2(3.0×106  eV)(0.511×106  eV)=3.57×1012  m=3.57  pmK = 3.0 \times 10^6 \;eV \\ E_0 = 0.511 \times 10^6 \;eV \\ λ = \frac{1240 \;eV \times nm}{\sqrt{(3.0 \times 10^6 \;eV)^2+2(3.0 \times 10^6 \;eV)(0.511 \times 10^6 \;eV)}} \\ = 3.57 \times 10^{-12} \;m \\ = 3.57 \;pm

For optical microscopes:

d=λ2NAd= \frac{λ}{2NA}

d is the resolution

λ is the wavelength

NA is the numerical aperture, which gathers light and resolve the specimen.

Where λ is the wavelength of light used to image a specimen. If using a green light of 514 nm and an oil immersion objective with an NA of 1.45, then the (theoretical) limit of resolution will be 177 nm.

d=5142×1.45=177  nmd= \frac{514}{2 \times 1.45} = 177 \;nm


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