198 5.5  Tools that Use Gamma Rays, Radioisotope Decays, and Neutrons

KEY POINT 5.3

Put very simply, there are just three types of high-​energy particles whose effective wave­

length is comparable to interatomic spacings in biological matter, which are electrons,

x-​ray photons, and neutrons and which thus can all be used in diffraction experiments

to generate information about the positions of atoms in biomolecules.

The other approach to generating thermal neutrons is to use spallation neutron sources.

These utilize particle accelerators and/​or synchrotrons to generate intense, high-​energy

proton beams, which are directed at a heavy metal target (e.g., made from tantalum) whose

impact can split the atomic nuclei to generate more neutrons. Proton synchrotron radiation

impacted on such a metal target can generate >10 neutrons from a nuclear reactor, with

an effective wavelength of ~10⁻¹⁰ m. Here, the scattering is due to interaction between the

atomic nuclei as opposed to the electron cloud.

Neutron diffraction has a significant advantage over x-​ray diffraction in that hydrogen

atomic nuclei (i.e., single protons) will measurably scatter a neutron beam, and this scatter

signal can be further enhanced by chemically replacing any solvent-​accessible labile hydrogen

atoms with deuterium, D, typically by solvating the target molecule in heavy water (D2O)

rather than normal water (H2O) prior to crystallization. This allows the position of the

hydrogen atoms to be measured directly, resulting in more accurate bond length predictions,

but with disadvantages of requiring larger crystals (length ~1 mm) and a nearby nuclear

reactor.

Small-​angle neutron scattering (SANS) uses elastic scattering of thermal neutrons by a

sample to generate structural information over a length scale of ~1–​100 nm. The principles

of operation are similar to SAXS performed with an incident x-​ray beam. However, since

neutrons scatter from atomic nuclei, unlike x-​rays, which are scattered from atomic electron

orbitals, the signal-​to-​noise ratio of diffraction intensity peaks is greater than SAXS for

lower-​atomic-​number elements. SANS has been applied to determine the structural details

of several macromolecular complexes, for example, including ribosomes and various bio­

polymer architectures such as the dendritic fibers of nerves in solution.

Worked Case Example 5.3: Radioisotope Decay

A radioisotope A contains a nucleus which decays with a constant λA, into another radio­

isotope B whose nucleus also decays but with a smaller constant λB into a stable isotope C.

a

If there are NA(0) initial atoms of A and none of B, determine a formula for the number

of atoms of B, NB(t), after time t.

b

A controlled experiment was performed to simulate the effects of radiation damage

to biological tissue during a nuclear reactor leak in which the ultimate product, iso­

tope Z with a half-​life ~20,000 years, is produced from a chain reaction involving the

radioactive decay of isotope X, which decays with a half-​life of 2.4 days to isotope Y

via beta decay, which in turn decays to Z also by beta decay but with a half-​life of 23.5

minutes. What percentage of the number of X atoms initially present will be Y atoms

after 1 hour?

Answers

a

The rate of change in number of B atoms is the rate of formation of B from A minus

the rate of decay of B into C. Using the general radiation decay Equation 5.27:

d

d

d

d

exp

A

A

A

A

A

A

A

A

N

t

N

N

N

t

N

t

N

t

A = −

∴

= −

∴

( ) =

( )

−(

)

∫

∫

λ

λ

λ

0

KEY BIOLOGICAL

APPLICATIONS:

RADIOISOTOPES

AND NEUTRONS

Tracking metabolic processes;

Determining macromolecular

structures.