Show that radioactive decay is an exponential process.State the laws of radioactive decay
Answers
Let's make it crisp and clear
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes.
Also,
How do we know that C14 decay's exponentially compared to linear
Here's an argument that might help: suppose, temporarily, that radioactive decay was linear. Let's say you started out with a sample, call it sample #1, of a billion atoms in a box, 5700 years ago (that's one half-life). By the current day, half of them would have decayed, so you'd have 500 million atoms left.
Now, let's say you take a different sample (sample #2) of 500 million atoms and put it in another box. Then wait 5700 years. According to the linear decay model, sample #1 would be entirely gone, but sample #2 would still have 250 million atoms. But if you think about it, that doesn't make sense, because if you jump back to the present, there is nothing to distinguish sample #1 from sample #2. Each of them consists of 500 million radioactive 14C atoms in a box. So there's no reason that sample #1 should behave any differently from sample #2. It doesn't "remember" that it came from an earlier sample of a billion atoms.
I'm not sure if it has been explicitly verified for carbon 14, but using other radioactive elements with shorter half-lives, it has been verified probably hundreds of thousands of times over the past century or so that they decay exponentially. It's a pretty simple experiment: you just measure the number of atoms that decay in a short interval of time Δt using a Geiger counter or something similar, then wait some time T>Δt, then again measure the number of atoms that decay in the interval Δt. The second measurement will give you fewer decays than the first, which is a sign of nonlinear decay. Making more measurements of this kind will reveal that the decay is exponential.
Radioactive law:
The radioactive decay law is an universal law that describes the statistical behaviour of a large number of nuclides.
The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. The radioactive decay of certain number of atoms (mass) is exponential in time.
Radioactive decay law: N = N.e-λt