"If the whole earth were one ball of carbon 14"

Let's first take the amount this means. Mass = volume * density.

Volume of earth 1.08321 × 10¹² km³
Density of graphite 2.09–2.23 g/cm

Let's translate the density a bit. 1000 g = 1 kg. 1000 (yes!) cm³ = 1 dm³.
1000 kg = 1 metric tonne, 1000 dm³ = 1m³

1 km = 10 * 1 hm
1 hm = 10 * 1 dkm (dekametre, not decimeter)
1 dkm = 10 * 1 m

For cubic versions, it' 1000 per transformation.

1 083 210 000 000 km³
1 083 210 000 000 000 000 000 m³

So, we are dealing with up to
1 083 210 000 000 000 000 000 m³ * 2.23 tonne/m³ = 2 415 558 300 000 000 000 000 tonnes

But this would be true if the tonnes were from Carbon 12. Carbon 12 has an atomic weight of 12, and Carbon 14 a bit above 14. This means the real weight of this would be 14/12 or 7/6 of above.

3 218 151 350 000 000 000 000 tonnes.

What does it take to get carbon 14 under 1 % of original amount? Let's check the halvings.

100.000 00 I
50.000 00 II
25.000 00 III
12.500 00 IV
6.250 00 V
3.125 00 VI
1.562 50 VII
0.781 25 VIII

That's 8 halvings, would take 8 halflives = 8 * 5730 = 45 840 years. Let's round the final result up to 0.8 % to make calculating a bit easier. And the Roman numerals from here on don't reer to halflives, but to "one of those" - that being the unit of 45 840 years.

25 745 210 800 000 000 000 tonnes after I
205 961 686 400 000 000 tonnes after II
1 647 693 491 200 000 tonnes after III
13 181 547 929 600 tonnes after IV
105 452 383 436.8 tonnes after V
843 619 067.494 4 tonnes after VI
6 748 952.539 955 2 tonnes after VII
53 991.620 319 641 6 tonnes after VIII
431.932 962 557 132 8 tonnes after IX
1.727 731 850 228 531 2 tonnes after X

From the graphite the volume of earth to less than 2 tonnes in 458 400 years.

1.727 731 850 228 531 2 tonnes =
1 727.731 850 228 531 2 kg =
1 727 731.850 228 531 2 g

I think we can ignore what's below 1 gram, let's round up

1 727 732 g for 1 727 731.850 228 531 2 g

13 821.856 g after XI
106.574 848 g after XII
0.852 598 784 g after XIII

So, graphite the volume of the earth is becoming less than one gramme in 13 * 45840, that is in 595 920 years.

Obviously, this weight refers to the weight of Carbon 14. As far as we know, it doesn't become nothing - but does it become carbon 12 or carbon 13 or nitrogen 14?

That's another question. At least after a bit more than half a million years, carbon 14 the volume of the earth would be reduced to less than one gramme. For purposes of carbon dating, the maximum actually used goes a few more halflives beyond 45840 years. I put in 70 000 years in a carbon 14 calculator, and I find "This date is too large and beyond the limits of present accuracy (55000 to 60000 years)" - and I also find, the actual value would be 0.021 pmC. If we then take 60 000 years as the limit, this means ones goes a bit beyond ten halvings, ten halflives. So, if something is carbon dated to younger than 60 000 years, it means there is measureable carbon 14 left. If there is measurable carbon 14 left, either it is in fact younger than 60 000 years, or it was contaminated. But contamination should be less omnipresent than to provide dates of 20 000 to 39 000 BP for dinosaurs when carbon dated consistently. It is more logical, they are in fact younger than 60 000 years, not older than 60 000 000 years. Especially as we do find human skeleta or associated material dated to earlier than that (like 50 000 years ago).

Hans Georg Lundahl
Paris
St. Catherine of Alexandria
25.XI.2022