Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  197

range of different radioisotopes that have direct biophysical application in acting as a source

of detectable radioactivity, which can be tagged onto a specific region of a biomolecule. This

radioactive tag therefore acts as a biochemical reporter or tracer probe.

The kinetics of radioactivity can be modeled as a simple first-​order process:

(5.27)

d

d

N

t

N

= −λ

where N is the number of radioisotopes of a specific type, with a decay constant λ. This

results in a simple exponential decay for N. The half-​life t1/​2 is the time taken to reduce N by

50%, which is simple to demonstrate as ln 2/​λ, while the mean lifetime of a given radioisotope

is given by 1/​λ.

The radioisotope is introduced in place of a normal relatively nonradioactive isotope,

typically to detect components or metabolites in a biological system in time-​resolved

investigations. Radioisotopes have relatively unstable atomic nuclei and their presence can

be detected from their emission of different specific types of radiation generated during

the radioactive decay process in which an energetic lower energy (i.e., more stable) atomic

nucleus is formed. The type of radiation produced depends on the isotope but can typically

be detected by a Geiger counter or scintillation phosphor screen, often in combination with a

CCD or PMT detector. In combination with stopped-​flow techniques, biochemical reactions

can be quenched at intermediate stages and the presence of radioisotopes measured in the

detected metabolites, which thus allows a picture of the extent of different biochemical

processes to be built up.

Common types of radiation emitted in radioisotope decay are gamma rays, beta particles

(high-​energy electrons), and alpha particles (⁴He²+​, in other words helium nuclei with no

atomic electrons). Alpha particles have a small depth of penetration (e.g., they are stopped by

just a few centimeters of air) and are thus not useful as tracers but find application in radio­

therapy. Common radioisotope tracers used in the life sciences include: ³H, ¹⁴C, ³²P and ³³P,

35S, 45Ca, and 125I. But 99mTc has a more focused application as a biomedical tracer. In addition,

a number of radioisotopes decay with output of a positron, which are relevant as biomedical

tracers in positron emission tomography, or PET (biomedical applications are discussed more

generally in Chapter 7).

5.5.3  NEUTRON DIFFRACTION AND SMALL-​ANGLE SCATTERING

Neutron diffraction works on similar principles to that of x-​ray diffraction but utilizing an

incident beam composed of thermal neutrons. Thermal neutrons can be generated by two

principal methods. One is to use a thermal nuclear reactor. These utilize the fission of the

235U isotope, which releases an average of ~2.4 extra neutrons for every fission event. An

example of ²³⁵U fission following neutron absorption is

(5.28)

n

n

+

→

→

+

+

U

U

U

K r

B

a+3

MeV

92

235

92

236

92

235

36

89

56

144

177

where just one of these released neutrons is required to sustain a chain reaction. Neutrons

formed from uranium fission have an average energy of ~2 MeV. These neutrons are slowed

down by a neutron moderator around the fission core (typically composed of water or

graphite) so that emergent neutrons are in thermal equilibrium with their surroundings

(hence, the term thermal neutrons), which have a mean energy of just ~0.025 eV with an

equivalent de Broglie wavelength of ~0.2 nm.