Lunar radioactivity

Creationists claim that, because the moon contains radioactive elements and "short-lived" isotopes, it cannot be old.

Isotopes
Evolution-Facts.org maintains, as of 2016:

One of the most surprising moon rock discoveries is seldom mentioned: Short-lived Uranium 236 and Thorium 230 were found in those stones! Short-term radioactive isotopes do not last long; they rather quickly turn into their end product, which is lead. If the moon were even 50,000 years old, these short-life radioisotopes would long since have decayed into lead. But instead they were relatively abundant in the moon rocks! The importance of this should not be underestimated. The moon cannot be older than several thousand years.

This is immediately incorrect. 230Th has a half-life of 75,380 years, and 236U has a half-life of 23,420,000 years. In 50,000, there would still be more than half (63.1%) of the original 230Th and almost all (99.85%) of the 236U. Even beyond this, we can expect measurable amounts of anything to hang around for about 10 half-lives, which pushes 230Th to 753,800 years, and 236U to 234,200,000 years.

Kent Hovind wrote:

The Moon contains considerable quantities of U-236 and Th-230, both of which are short-lived isotopes that would have expired long ago if the Moon were 4.5 billion years old.

R. L. Wysong 1976 writes:

Th-230 and U-236 exist on the moon. But these isotopes are so short-lived that we would not expect any still to be around if the moon were billions of years old.

Indeed, if the Earth and Moon are indeed 4.5 billion years old, no trace of the original supply of those isotopes should now exist.

Where does the 230Th come from? The most abundant uranium isotope is 238U, about 99.275% of natural uranium. 238U decays until it ends up as 206Pb, lead. 238U has a half-life of 4,468,000,000 years, already long enough to be compatible with an old moon. Creationists assume that the 230Th had to be there from the beginning, but instead 230Th is continuously created.

Where does the 236U come from? The next most abundant uranium isotope is 235U, about 0.7% or 0.72% of natural uranium. 235U has a half life of 703,800,000 years, but using the 10 half-life criterion, measureable amounts should hang around for about 7,038,000,000 years, again long enough for an old moon. The lunar surface is directly exposed to solar wind and other sources of cosmic rays. 235U will turn into 236U by absorption of a single slow neutron, which can be supplied directly by solar wind or as a by product of a solar wind proton colliding with the lunar surface. Creationists assume that the 236U had to be there from the beginning, but instead 236U is continuously created.

Thus, the Th-230 and U-236 we see on the Moon are of recent origin, not part of the Moon's primordial supply, and therefore do not constitute evidence for a young Earth.

Even CreationWiki agrees that this is a bad argument.

Radioactivity
Evolution-Facts.org maintains, as of 2016:

Rocks brought by Apollo teams from the moon have been dated by the various radiometric methods. A variety of very conflicting dates has resulted from these tests (see chapter 7, Dating Methods, for a discussion of this). But the factor of relatively high radioactivity of those rocks indicates a young age for the moon[.]

Kofahl et al. 1975 wrote:

The content of radioactive elements in the moon rocks is so high that if the moon were actually millions of years old, the heat produced by radioactive decomposition would have melted the moon.

Yet radioactivity is the direct product of the breakdown of short half-life isotopes; as long as there is a source for these radioisotopes (and such a source was proven above), then there is no issue here.