There is a lot of discussion about this issue on this internet, so I think this question may be worth addressing seriously.The main point of the debate seems to be the following: Over the past decades, several research groups of self-proclaimed creationist scientists have claimed discoveries of dinosaur bones that they have managed to date, using radiocarbon dating methods, at some age which is a lot below the 'usual' i.e.The particular example you bring up is one of the most famous such cases.

Now, it is known that $^\text$ decays at a fast enough rate (half-life ~6000 years) for this dating method to be absolutely useless on such samples. would not have been able to obtain this sample, had they been honest about their intent.

This, of course, raises some ethical questions, but let's brush these aside for now.

And the result of this accepted method dates dinosaur fossils to around 68 million years old. Its half-life ($t_$) is only 5,730 years—that is, every 5,730 years, half of it decays away.

The theoretical limit for C-14 dating is 100,000 years using AMS, but for practical purposes it is 45,000 to 55,000 years.

“Seldom has a single discovery in chemistry had such an impact on the thinking in so many fields of human endeavour,” one of Libby's colleagues wrote at the time, according to the Nobel Foundation.

Today, carbon dating is used so widely as to be taken for granted.

What solutions are available for increasing accuracy of the tests? From the source linked above: Carbon-14 is considered to be a highly reliable dating technique.

It's accuracy has been verified by using C-14 to date artifacts whose age is known historically.

We proceed with the examination of the research done by Miller and his fellow researchers from the CRSEF.

At a horizon of 40,000 years the amount of carbon 14 in a bone or a piece of charcoal can be truly minute: such a specimen may contain only a few thousand 14C atoms.

That included protecting the samples, avoiding cracked areas in the bones, and meticulous pre-cleaning of the samples with chemicals to remove possible contaminants.

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