Were Adam and Eve Toast?
by Joe Meert
(created 1996, Updated March 2002)

One of the issues in the creation/evolution debate is the claim that radioactive decay is not constant. In order for the Earth to appear old, creationists must assume that radioactive decay rates in the past were faster. This solves the problems of old ages in rocks, but unfortunately opens up a bigger problem. Radioactive decay gives off heat. The amount of heat generated is proportional to the rate of decay and the amount of radioactive material present at the time. In the following exercise, I show how much heat can be generated by radioactive decay IF decay rates were faster in the past.  Please note that the following analysis uses present-day heat production values which are observable quantities and I have also assumed (in the creationist analysis) that each of the elements has the same rate of decay.  Changing the decay rates to those observed today for each of the major heat producing elements makes the mathematics a bit more tedious, but does not significantly alter the conclusions given here.  SPECIAL ADDED NOTE: Several creationists have suggested that I did not identify my starting assumptions and asked how much daughter was initially present?   This question, while interesting in the general discussion of the age of a rock sample, is irrelevant to this exercise.  I am discussing solely the amount of heat produced by decay rather than the age of a particular rock unit. 

Present day of heat production from radioactive decay in the Earth is produced mainly by the isotopes 238U, 235U, 232Th and 40K and has a value of 6.18 x 10-12 W/kg (Turcotte and Schubert, 1982). If the heat flow out of the Earth were due solely to radioactive decay in the mantle and crust, it would equal:

Heat Production * (Mass of Mantle + Crust)

6.18 x 10-12 W/kg * 4.0 x 1024 Kg = 2.47 x 1013 W (Eqn 1)

the heat flow out of the Earth can be calculated from Fourier's Law of heat conduction:

                                Q = k dt/dz, where:

k = thermal conductivity of the rocks W/m oC
dt/dz = geothermal gradient (change in temp with depth)
Q= W/m2

To calculate the surface heat flow, we divide the result from Eqn 1 by the total surface area of the earth (5.1 x 1014 m2)

2.47 x 1013 W / 5.1 x 1014 m2 = .048 W/m2 (Eqn 2)

If we now use this to calculate the temperature-depth profile dt/dz, we need to use an average value of thermal conductivity.  I use 3.00 W/m oC as an average thermal conductivity of the rocks.   This yields:

dt/dz = .048 W/m2 / 3 W/m oC = 16 oC/km (Eqn 3)

Thus, for every 1 kilometer depth, the temperature will increase by about 16 oC.  Special Note: As you get deeper into the crust and mantle, temperature increases are not linear because they are a function of pressure and other factors. Nevertheless, this relationship is useful to depths of 30-70 kilometers. Therefore, at a depth of 10 kilometers, the temperature would be about 160 oC.   Basaltic rock melts at about 1200 oC.  There are some simplifications made in the above calculations since much of the heat production (~67%) is confined to the crust, but the illustration below is useful regardless of this simplification.

Let's look at these same relationships with a much younger earth and a faster rate of decay.  In my example, I will use a 'standard' creationist age for the earth of 6000 years.  In order to carry out the analysis, we must still assume some sort of decay 'constant'.  There are a number of ways this could be done, but the simplest is to assign an average half-life.  I will use 500 years as the average life for the radioactive elements listed above. In reality, I am being OVERLY generous to the young Earth crowd.  If rates were variable, they would probably have been much faster than this and the resultant earth conditions would be more extreme.  The interested reader can easily play with the variables on a spreadsheet and see how they affect the conclusions reached below.  Special Note: It is possible, though more tedious to calculate the heat release using a decelerating decay rate.   It does not change the basic conclusion reached in the following exercise.  In order to do this, one simply replaces l with a function e-rate.

In order to figure out the rate of heat production in the past, we must first calculate a decay constant lambda (l). This is calculated from

t = ln 2 / l

or l = ln 2 / t

using 500 years for t , we get l = 1.38 x 10-3.

The rate of heat production at any time in the past is given by the following formula (Turcotte and Schubert, 1982):

Hpast = Hpresent * e l (t-t0)

we use Hpresent = 6.18 x 10-12 W/kg

and t-t0= 6000 years and l as calculated above and we get:

Hpast = 2.43 x 10-8 W/kg

We can now use this value to calculate the amount of heat flow out of the Earth due solely to this ancient (6000 year old) heat production and calculate a thermal profile as we did above in Eqn 1 and 2.

Hpast * (Mass of Mantle + crust) = total heat production

Hpast = 2.43 x 10-8 W/kg * 4.0 x 1024 kg = 9.75 x 1016 W

We now divide this value by the surface area of the Earth to get the heat flow Q at 6000 years ago.

Q = 9.75 x 1016 W / 5.1 x 1014 m2 = 191 W/m2

Using the same value for thermal conductivity 3.00 W/m oC, we can calculate the dt/dz profile as above in Eqn 3:

191 W/m2 / 3.00 W/ m oC = 65,000 oC/ km!!

    At 6000 years ago, it is pretty obvious that the entire Earth would be molten and Adam and Eve's goose was cooked.  I must also add that because of these extreme temperatures, a purely conductive heat regime is implausible.  I am not implying that this is a purely conductive regime. What I am showing is that the thermal regime on a 6000 year old earth with rampant radioactive decay is extreme. If you want to turn off the engine and let the Earth cool from this extreme you also run into time spans much greater than 6000 years because it will take a while to cool down from those extreme temperatures. It's difficult to estimate how long it would take for the Earth to reach present-day temperatures because I frankly don't know where the creationists would take their argument. It is clear that rapid decay results in a tremendous release of heat. I suppose you could always argue that the Earth has been cooling since this initial heating and that there is no further significant heat released by radioactive decay. In that case, the cooling of the Earth reduces to the Kelvin problem and gives an age of 20-60 million years.   The graph below gives some of the major events in Creationist history along with the geothermal gradient.   Special Note: Some creationists have argued that the graph below should not be projected as semi-log linear past the Noachian flood.  Of course, this is simply based on at least two unsupported asserttions: (a) That a global flood occurred and (b) that some miraculous change in physical conditions occurred.  Neither assumption can be supported with data.   Nevertheless, if one assumes that there was some fundamental change in physical law post-flood, it does not resolve the heat problem described here.

adam.jpg (38488 bytes)
Note the Scale is semi-logarithmic.

Additional Notes/Updates

(a) I did a rough calculation for the Earth's conductive profile using the old Earth model and the average geothermal gradient 3.5 billion years ago is about 27 oC/km.

(b) Just for those who are interested, if Noah's flood took place about 4000 years ago, this calculation yields roughly 40,000 oC/km. Guess what? Maybe there was a vapor canopy anyway since liquid water would not be present!!

(c) At the time of Jesus' birth, the geothermal gradient would have been ~400 oC/km.

Note: Several creationists have commented that the calculations would not be correct if the speed of light has decayed over the past 6000 years.  This is due to the fact that the speed of light factors into radioactive decay equations/energy.  At present, there is no evidence to suggest that the speed of light (in vacuo) is a variable.   Until such a time when this assertion can be substantiated with real data, the argument stands testament to one of the major problems associated with rapid decay proposals.   In fact, 'creation scientists' at the Institute for Creation Research have noted:

"One major obstacle to accelerated decay is an explanation for the disposal of the great quantities of heat which would be generated by radioactive decay over short periods of time. For example, if most of the radioactive decay implied by fission tracks or quantities of daughter products occurred over the year of the Flood, the amount of heat generated would have been excessive, given present conditions."

Special Note: Several creationists assert that I am ignoring miraculous behavior in this analysis.  Guilty as charged.  Science must be based solely on the evidence available.  One could argue a whole series of miraculous events, but none of these have supporting evidence.  It seems much easier to accept that if God created the earth and gave man the ability to think about the earth, HE/She or it would also not have created fake evidence.

Joe Meert
e-mail: jmeert@geology.ufl.edu

In a recent e-mail discussion, I was asked why the earth is still tectonically active whereas Mars, Mercury and the Moon are not.  The assumption was that if the accretionary model for the solar system was correct, then each of the planets would have received more or less an equal amount of radioactive material.  In fact, this assumption is certainly reasonable for the inner planets and our Moon.  The person asking the question seemed to think that if this assumption was correct, then Mars should show activity (active heat release on the surface).  Mars does not seem to show any recent activity although, it still retains some heat, but not enough to make the surface dynamic.  Ditto for the Moon and Mercury.  All of these moons and planets show evidence of past activity.  We can, quite simply estimate the average surface heat flow for these planets assuming they had the same primordial composition of the earth.   Here is a table of results for each of the inner planets.  As you can see, Earth and Venus produced have a much higher heat flux than their smaller neighbors.   The calculations suggest that surface expressions of this heat release are most likely to be on the 'hotter' planets which is exactly what is observed.  

Planet Name Radius (km) Mass (Mantle+Crust)* Heat Production (Watts) Surface Area (m2) Heat Flux (W/m2) Geothermal Gradient (C/km)
Moon 1738 4.96E+22 3.06528E+11 3.79585E+13 0.008075338 2.691779371
Mars 3398 4.31E+23 2.66358E+12 1.45096E+14 0.018357313 6.119104209
Earth 6378 4.00E+24 2.472E+13 5.11186E+14 0.048358135 16.11937838
Mercury 2439 2.23E+23 1.37814E+12 7.47538E+13 0.018435709 6.145236348
Venus 6050 3.26E+24 2.01468E+13 4.59961E+14 0.043801142 14.60038067

*Ratio of mantle+crust mass to total mass for each planet was considered a constant.

Refs: 1. Turcotte & Schubert, 1982, Geodynamics, John Wiley and Sons