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

6.18 x 10

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

k = thermal conductivity of the rocks W/m

dt/dz = geothermal gradient (change in temp with depth)

Q= W/m

To calculate the surface heat flow, we divide the result from

2.47 x 10

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

dt/dz = .048 W/m

Thus, for every 1 kilometer depth, the temperature will increase by about

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 ½ 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

t ½ = ln 2 / l

or l = ln 2 / t ½

using 500 years for t ½ , we get l = 1.38 x 10

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

H

we use H

and t-t

H

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

H

H

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 10

Using the same value for thermal conductivity 3.00 W/m

191 W/m

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

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

(b) Just for those who are interested, if Noah's flood took place about 4000 years ago, this calculation yields roughly 40,000

**(c) At the time of Jesus' birth, the geothermal gradient would have been ~400 ^{o}C/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."

Cheers,

Joe Meert

e-mail: jmeert@geology.ufl.edu

Planet Name | Radius (km) | Mass (Mantle+Crust)* | Heat Production (Watts) | Surface Area (m^{2}) |
Heat Flux (W/m^{2}) |
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 |

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