Question

When aboveground nuclear tests were conducted, the explosions shot radioactive dust into the upper atmosphere. Global air circulations then spread the dust worldwide before it settled out on ground and water. One such test was conducted in October 1976. What fraction of the ${}^{90}Sr$ produced by that explosion still existed in October 2006? The half-life of ${}^{90}Sr$ is 29 y.

Answer 1

(a) Our calculation is identical to that in Sample Problem — “Fusion in a gas of protons and required temperature” except that we are now using R appropriate to two deuterons coming into “contact,” as opposed to the $R=1.0fm$ value used in the Sample Problem. If we use $R=2.1fm$ for the deuterons, then our K is simply the K calculated in the Sample Problem, divided by 2.1:
$k_{d+d}=\frac{k_{p+p}}{2.1}=\frac{360keV}{2.1}\approx 170keV$
Consequently, the voltage needed to accelerate each deuteron from rest to that value of K is 170 kV.
(b) Not all deuterons that are accelerated toward each other will come into “contact” and not all of those that do so will undergo nuclear fusion. Thus, a great many deuterons must be repeatedly encountering other deuterons in order to produce a macroscopic energy release. An accelerator needs a fairly good vacuum in its beam pipe, and a very large number flux is either impractical and/or very expensive. Regarding expense, there are other factors that have dissuaded researchers from using accelerators to build a controlled fusion “reactor,” but those factors may become less important in the future — making the feasibility of accelerator “add-ons” to magnetic and inertial confinement schemes more cost-effective.