Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  163

energy qV, where q is the magnitude of the unitary charge on the electron (~1.6 × 10⁻¹⁹ C)

being accelerated through a voltage potential difference V (a broad range of ~0.2–​200 kV

depending on the specific mode of EM employed):

(5.1)

E v

E

qV

( ) −

( ) =

0

The relativistic relation between an electron’s rest mass m0, ~9.1 × 10⁻³¹ kg, its momentum p,

and its energy given by the energy-​momentum equation,

(5.2)

p c

E v

m c

2

2

2

0

2

2

=

(

) −(

)

But the wavelength of the accelerated electron can be determined from the de Broglie rela­

tion that embodies the duality of waves and particles of matter, which on rearranging yields

(5.3)

λ=

/

h

p

h

m qV

qV

m c

=

−

+(

)

2

1

1

2

0

0

2

where h is Planck’s constant ~6.62 × 10⁻³⁴ m² kg s⁻¹. Thus, the usual classical approximation

(cited in many textbooks)

(5.4)

λ ≈

h

m qV

2

0

still holds to within ~10%. Typical accelerated electrons have such matter wave wavelengths

of 10⁻¹² to 10⁻¹¹ m, and waves will exhibit wavelike phenomena such as reflection and

diffraction.

The hypothetical spatial resolution Δx of an electron beam probe is diffraction limited

in the same sense as discussed previously in Chapter 4 for a visible light photon beam

probe, which is determined by the Abbe diffraction limit for circularly symmetrical imaging

apertures of ~0.61λ/​NA. For a high-​resolution (i.e., short wavelength) electron microscope,

which might accelerate electrons with ~100 kV, the wavelength λ is ~4 × 10⁻¹² m, whereas

the effective numerical aperture, NA, is ~0.01. This would imply an Abbe limit of ~0.2 nm

for spatial resolution. However, in practice, the experimental spatial resolution is an order of

magnitude worse than would be expected from the Abbe limit at a given wavelength, which

is more like 1–​2 nm in this instance, mainly due to the limitations of spherical aberration on

the electron beam, but also compounded by the finite size of scattering objects used as typ­

ical contrast reagents and of spatial distortions to the sample cause by the method of fixation.

5.2.2  FIXING A SAMPLE FOR ELECTRON MICROSCOPY AND GENERATING

CONTRAST

The ultralow pressures used in standard electron microscopes would result in rapid, uncon­

trolled vaporization of water from wet biological samples, which would result in sample

degradation. The specific methods of sample preparation differ depending on the type of

EM imaging employed. For example, cryo-​EM (discussed in detail later in this chapter) has

distinctly different preparation methods compared to transmission EM and scanning EM

techniques. Also, the method of preparation depends of the length scale of the sample—​

whether one is fixing an entire insect, a cell, a subcellular cell compartment, a macromol­

ecular complex.

Tissue samples prepared for EM are fixed so as to prevent uncontrollable water loss,

through either dehydration or freezing, and are often fixed to lock the movement of the