Assume Twice the Halflife ...

Creation vs. Evolution Am I Wrong in Assuming a Stable C14 Level for Last Millennia? · So, What Are the Possible Solutions? · New blog on the kid : Assume Twice the Halflife ... · So, Doubling the Halflife and Assuming a Rising C14 Level Doesn't Fix It ...

Warning, this is very technical. You had better read previous parts first.

I

1950 AD + 1185 BC = 3135 years
68.438 % in the normal decay rate and therefore 68.438 pmC in samples from then.

1567.5 - with twice the halflife, the time gives just the decay for half the time.

82.728 % instead of 68.438 %.

x * 82.728 / 100 = 68.438
x = 68.438 / 82.728 * 100
x = 82.727 pmC

How much faster is C14 produced then than I expected?

After 3135 years
82.727 pmC * 82.728 / 100 = 68.438 pmC

B u t we have 100 pmC

Production in 3135 years therefore 100-68.438 = 31.562 pmC

"Normal" production (generally assumed with 5730 = 50 %) 100 pmC => 68.438 pmC + 31.562 pmC new, production rate equal ...

II

3135 / 2 = 1567.5 - I am here adressing the actual years, not the reduced decay rate within the longer span.

What would happen in each half? A) With normal production rate? B) With known remainders from 1567.5 years ago?

II A

In 1567.5 years, the decay with doubled halflife would be that of 783.75 years as per halflife 5730 ... 90.955 % and the production rate would be that of our normal 100 - 82.728=17.272 pmC points.

Start out 1185 BC, 82.727 pmC

82.727 * 90.955 / 100 = 75.244 pmC
75.244 + 17.272 = 92.516 pmC

This 92.516 pmC back in 382 or 383 AD would undergo a decay of 90.955 % giving:

92.516 * 90.955 / 100 = 84.148

We would be dating that as 84.148 pmC = 1450 years old, 1950 - 1450 = 500 AD ... 117 to 118 years too recent. But Minze Stuiver (see previous parts!) say that the carbon age for 380 AD is 1950 - 1700 = 250 AD.

Then, second half, the

92.516 * 90.955 / 100 = 84.148 pmC
84.148 + 17.272 = 101.42 pmC

in 1950, except that CO2 emissions diluted that. But less than expected.

II B

Start out 1185 BC with 82.727 pmC

Get to 383 AD with y ... which is such that with double the halflife we get to a date that is 1700 carbon years old or a sample with 81.412 pmC.

y * 90.955 / 100 = 81.412 pmC
y = 81.412 pmC / 90.955 * 100
y = 89.508 pmC

So, in order to get to 89.508 instead of to 92.516 pmC, we have to add ...

92.516 - 89.508 = 3.008
17.272 - 3.008 = 14.264 pmC

... we have to add 14.264 pmC. This means, the added production is 14.264 instead of 17.272 pmC.

14.264 / 17.272 = 0.826 times as fast.

Then ...

383 AD with 89.508 pmC
89.508 pmC * 90.955 / 100 = 81.412 pmC

81.412 + 17.272 = 98.684 pmC
81.412 + 14.264 = 95.676 pmC

And the actual level in 1950 is between these, 97.61 pmC (analysis of Minze Stuiver*) . No accounting for the diluting effect.

III

Now, let's compare the production coefficients between Flood and Fall of Troy for A) halflife 5730 years (as normally presumed) and for B) halflife 11460 years (as I am discussing here).

III A

2957 BC 1185 BC
1.4 pmC 100 pmC

2957 - 1185 = 1772 years

Normal production 1772 years = 100 pmC - 80.706 % = 19.294 pmC

Production those 1772 years

1.4 pmC * 80.706 / 100 = 1.13 pmC
100 - 1.13 = 98.87 pmC

98.87 pmC / 19.294 pmC = 5.124 as fast.

III B

A sample from 2957 BC normally in 1950 has 2957+1950 = 4907 => 55.234 % of original level.

1.4 pmC * 55.234 / 100 = 0.773 pmC

Now, assume we get the 0.773 pmC from an original z with instead halflife 11460 ...

4907 / 2 = 2453.5 => 74.32 %

z * 74.32 / 100 = 0.773
z = 0.773 / 74.32 * 100 = 1.04 pmC

Now, how would we get from 1.04 pmC at Flood to 82.727 pmC at Fall of Troy?

Decay 1772 / 2 = 886 => 89.837 %

1.04 pmC * 89.837 / 100 = 0.935 pmC

82.727 - 0.935 = 81.792 pmC

81.792 pmC / 19.294 pmC = 4.239 times as fast.

Conclusions:

• assuming a halflife of 11460 years and a C14 level still rising will not make the production at present exceed normal so much as to counterbalance the diluting influence presumed by CO2 emissions if entirely fossil;
• it will make the rise from Flood level to Troy level somewhat less radical, 4.239 rather than 5.124 times the normal production;
• it could arguably be disproven by, 72 years after 1950, showing samples from then preserved to now have 99.133 % and not 99.565 % of the original level**, as ascertained back then from comparable samples. The former being the decay for 72 years, the latter for 36 years as per assuming twice the length of the halflife.

Hans Georg Lundahl
Paris
St. John Bosco
31.I.2022

* Minze Stuiver and Bernd Becker, sorry!

** Note, I said of original level, not of 100 pmC, since the general carbon level in 1950 was not 100 pmC pre-industrial levels.