Let’s get back to the science.
Evidently as a follower of the world/carnal /opposed to God / "false science" type of science, I need to explain a common YEC argument regarding half-lives that one needs to hang around for the half life of an element in order verity it is correct.
Obviously for elements such as ²³⁸U which has a half-lie of around 4.5 billion years this is not terribly practical.
Let’s look at an analogy of a car travelling at a
constant velocity of 100 km/hr.
In order to verify the speed on the speedometer, do we need to travel 100km to measure the time taken or alternatively travel for 1 hr and measure the distance covered?
Clearly the answer is no since the distance-time (s-t) relationship is a straight line with a constant gradient which is the velocity and we can arbitrarily select a distance or time interval of any magnitude to calculate the velocity v.
In the case radioactive decay there is a straight line relationship between the decay rate dN/dt and the amount of radioactive material present N.
The gradient of the line depends on the decay constant k in the equation
The half life t(1/2) is given by the equation;
Nₒ is the initial amount a t=0.
Since there is a straight line relationship using a half life is not compulsory where 50% of atoms have decayed, we could easily use any other time interval such as where only 1% of atoms have decayed in which case the equation becomes.
The other question thrown up by YECs is the decay rate k being different in the past, this not a scientific question but a question in hope that a 6000 year old earth is supported by a false dichotomy.
The scientific answer is k only changes when the parent atom has decayed into a daughter atom which also undergoes decay for example;
²³⁸U → ²³⁴Th → ²³⁴Pa
50% of uranium-238 decays into thorium-234 in 4.5 billions years but 50% of thorium-234 only takes 24 days to decay to protactinium-234m.