Other newer techniques that may find increased usage in the future are exemplified by the method for activation analysis of the whole human body. The use of neutrons produced by nuclear machines (such as cyclotrons or other particle accelerators) or produced by compact, portable isotopic sources will make neutron activation analysis even more versatile. Isotopic sources produce neutrons as the result of a nuclear reaction. One such reaction uses alpha particles emitted by polonium-210 (or some other alpha emitter) to bombard the element beryllium. A different kind of isotopic source is the man-made radioisotope californium-252 that decays by fissioning (splitting) spontaneously and produces neutrons in the process. (One milligram of californium-252 will spontaneously produce over 10⁹ neutrons per second.) While californium-252 is quite expensive at present, it is likely that production costs will be significantly reduced in the future. With computers, more convenient radiation sources, and continuing improvements in the technology of gamma-ray detectors and nuclear electronics, neutron activation analysis will become more and more a routine tool of the analyst. APPENDIX Calculation of arsenic concentration with no standard for comparison. 1. Determination of arsenic-76 activity produced from _1_ microgram of arsenic at the time it comes out of the reactor. We use the equation from page 12: A₀ = Nφσ (1 - e^{-λt}) where N is the number of target atoms. (One microgram of arsenic contains (10^{-6} gram/75 grams per mole[12]) × 6.02 × 10²³ atoms per mole which is 8 × 10¹⁵ atoms of arsenic.) φ is the neutron flux. (This would be known to the reactor operator. It is usually measured by inserting materials of known composition and measuring their activation. In this case, φ = 10¹³ neutrons per square centimeter per second.) σ is the activation cross section. (Neutron cross sections have been measured and tabulated by scientists. For the activation of arsenic-75 to arsenic-76, the cross section is known to be 4.2 × 10^{-24} square centimeter.) λ is the disintegration constant for arsenic-76. (Here, λ = (ln 2[13]/t_{½},(in hours); t_{½}, the half-life for arsenic-76, is 26.6 hours so λ = (0.693/26.6) = 0.026.) t is the time of the irradiation. (Here t is 12 hours.) Therefore: A₀, the activity of arsenic-76, = 8 × 10¹⁵ × 10¹³ × 4.2 × 10^{-24} × (1 - e^{-0.026 × 12}) (Note: e is a physical constant, 2.71+) = 9 × 10⁴ disintegrations per second per microgram 2. Determination of activity of arsenic measured in the sample and corrected back to the time of removal from the reactor. We use the equation: A₁ = (R)/(E × F) e^{λt} where R is the measured count rate. (In this case, R is the number of counts per second observed in the 0.559-MeV gamma-ray peak, which is 5300 counts in 20 minutes or 4.4 counts per second.)