The idea of turning lead into gold has fascinated alchemists and scientists for centuries. While it is not feasible to do this through traditional alchemical methods, modern nuclear physics has made it possible to transmute elements. This process involves bombarding lead with high‑energy particles, causing it to lose protons and neutrons, ultimately transforming it into gold.
The process is not practical for large‑scale production of gold due to the immense energy required and the low yield of gold produced. However, it serves as a fascinating example of the principles of nuclear physics and the potential for manipulating matter at the atomic level.
Suppose we have a lead pellet (Pb‑208) that is 2 cm thick with a diameter of 4 cm. We bombard it with protons to transmute it into gold (Au‑197). The proton beam has a current of 100 µA and an energy of 1 GeV, and we assume the beam is entirely absorbed in the pellet. The lead density is 11.34 g cm−3 and its molar mass is 207.2 g mol−1. We want to know how long to irradiate the pellet to obtain 0.1 ozt (troy ounce) of gold.
The reaction is written as
p + 20882Pb → 19779Au + 4 p + 8 n
or, compactly, 20882Pb(p,4p+8n)19779Au.
The first step would be to find the desired gold mass in grams (g) so that everything is in SI units: \[ m_{Au}=0.1\,\text{ozt}=0.1\times31.1035\,\text{g}=\mathbf{3.11035\;g}. \] If we want to transform the lead into gold, the number of Au‑197 atoms that would be produced is: \[ N_{Au}=\frac{m_{Au}}{M_{Au}}N_{A}=\frac{3.11035\,\text{g}}{197\,\text{g mol}^{-1}}\,(6.022\times10^{23}\,\text{mol}^{-1}) =\mathbf{9.51\times10^{21}\;\text{atoms}}. \]
Notice that in the equation for the nuclear reaction above, 1 Au atom gets produced for 1 proton striking 1 Pb atom. Ergo, it will be useful for us to know the proton flux for the 100 µA beam, which is the number of protons per second striking the target. The current \(I\) in amperes (A) is defined as the charge per second: \[ \dot N_{p}=\frac{I}{e}=\frac{1.00\times10^{-4}\,\text{C s}^{-1}}{1.602\times10^{-19}\,\text{C}} =\mathbf{6.24\times10^{14}\;\text{p s}^{-1}}. \]
Since the proton beam is striking the surface of the target, it is crucial to know the surface density, or areal density, of the Pb‑208 target nuclei (pellet thickness t=2 cm): \[ n_{t}=\frac{\rho_{Pb}\,t}{M_{Pb}}N_{A}=\frac{11.34\,\text{g cm}^{-3}\times2\,\text{cm}}{207.2\,\text{g mol}^{-1}} \,(6.022\times10^{23}\,\text{mol}^{-1})=\mathbf{6.59\times10^{22}\;\text{cm}^{-2}}. \]
Production rate of Au‑197 via the direct channel is \[ \dot N_{Au}=\dot N_{p}\,n_{t}\,\sigma_{(p,4p8n)}, \] so that the irradiation time becomes \[ t_{irr}=\frac{N_{Au}}{\dot N_{Au}}= \frac{9.51\times10^{21}}{6.24\times10^{14}\,\times6.59\times10^{22}\,\times\sigma}\;\text{s} \;=\;\frac{2.31\times10^{-16}}{\sigma}\;\text{s}, \] where \(\sigma\) is the reaction cross‑section in cm2.
Example. If the direct cross‑section at 1 GeV is, say, 1 millibarn \((1\,\text{mb}=1.0\times10^{-27}\,\text{cm}^2)\), then \[ t_{irr}=\frac{2.31\times10^{-16}}{1.0\times10^{-27}}\;\text{s}\approx2.3\times10^{11}\,\text{s}\;\approx7.3\times10^{3}\,\text{years}. \] Even for a ten‑times larger cross‑section of 10 mb the time would still be of order centuries, illustrating why proton‑driven transmutation is not a commercially viable path to gold.
A nuclear clock keeps time by locking a laser to an energy jump inside the atomic nucleus rather than to one of the electronic hops that underpin modern atomic clocks. The transition scientists have homed in on is the ultra-low-energy \(8.19\text{ eV}\) isomeric excitation in \(\,^{229}\text{Th}\).
To realise this idea, researchers follow two complementary routes. One traps and sympathetically laser-cools single \(\text{Th}^{3+}\) ions inside a cryogenic radio-frequency Paul trap; the other embeds billions of thorium nuclei in wide-band-gap crystals such as CaF\(_2\) or LiSAF, letting the solid host hold the sample. In both cases a vacuum-ultraviolet clock laser, phase-locked to a femtosecond frequency comb, repeatedly drives the nuclei between the ground state and the long-lived isomer. A feedback loop locks the laser precisely on resonance, and counting its optical cycles delivers the tick of the clock.
Because nuclear energy levels sit deep inside the atom and are screened by surrounding electrons, the transition is largely immune to stray electric, magnetic, and thermal fields, pointing toward fractional uncertainties below \(10^{-19}\). Recent spectroscopy has pushed the effective linewidth into the few-hundred-hertz range and pinned the absolute transition frequency to kilohertz precision, bringing a working thorium nuclear optical clock—and applications that range from relativistic geodesy to stringent tests of fundamental constants—within reach.
(Work in Progress)
Bell's inequalities are a set of inequalities that serve as a test for the predictions of quantum mechanics against those of classical physics. They were derived by physicist John Bell in 1964 and have been experimentally tested in numerous experiments since then. The essence of Bell's theorem is that if local hidden variables exist, then certain statistical correlations predicted by quantum mechanics cannot be observed.
(Work in Progress)