Hey guys!
In this new video, we're going to take a look at radioactive decay rates.
We’re going to say when it comes to radioactive decay, it’s going to follow a first-order
mechanistic step.
We’re going to say here it's a first-order process whose rate is proportional to the
number of radioactive nuclei N, where k is a first-order rate constant called the decay
constant.
This kind of follows what we learned earlier when it comes to kinetics.
If you’ve seen my earlier videos on chemical kinetics, you should be very familiar on how
exactly we’re going to solve these types of questions because when it came to chemical
kinetics, we did the Integrated Rate Laws.
We’re going to say when it comes to radioactive decay, we're going to basically follow those
Integrated Rate Laws just a little bit differently.
When it comes to kinetics, we’re going to say that Rate Law equals our rate constant
k times the concentration of our reactant to some power.
That power we call a reaction order.
Since we’re dealing with radioactive systems now, it's basically this equation just changed
a little bit.
Here we still have rate but instead of saying Rate Law, we’re saying Decay Rate.
Here, this is our rate constant k but now it’s our decay constant k.
Here, this was the concentration of our reactant, but now it's the concentration of our radioactive
nuclei.
Similar but yet different.
Now, we’re going to say again radioactive decay follows a first-order process like I
said earlier.
Here we’re just going to reuse the first-order integrated rate law from the chapter on chemical
kinetics.
Remember, kinetics just looks at rate or speed of reactions.
We're looking at how quickly do my reactants break down to give me a product.
But since we're talking about radioactive systems now, we’re saying how quickly will
my radioactive compound breakdown.
That’s just the fundamental difference.
In regular kinetics, we’re looking at how fast the reactant basically becomes product.
Here we're looking at how fast is my radioactive compound just decay away.
Here, when we dealt with chemical kinetics, we said that the integrated rate law for the
first-order process was ln of my final concentration of my reactant equals negative rate constant
times time plus ln of the initial concentration of my reactant.
Again, this was your final concentration of your reactant.
This right here was your rate constant.
Here this was your time and here this was the initial concentration of your reactant.
Since we're going to need some room guys to finish writing all that notes that we need,
I'm going to remove myself from the image.
Remember, this was in chemical kinetics, the first-order integrated rate law.
But now we're dealing with radioactive systems, so the equation is going to change a little
bit.
Here we’re going to have ln Nt.
Here.
Nt stands for what?
We're going to say here Nt stands for the final concentration of our radioactive nuclei.
Just think of it as your radioactive reactant.
Radioactive nuclei is equivalent in a sense to your radioactive reactant.
That equals negative kt plus ln of No.
You can see that they're very similar.
All we’re really doing is substituting in N and replacing the variable A. That’s the
only real difference here.
Here instead of this being our rate constant, it's going to be now our decay constant.
Here this is still time.
Here, this would just represent your initial concentration
of your radioactive nuclei.
But they're very similar equations.
If you know how to use the one from the chemical kinetics chapter, then you’ll have no problem
adopting it to these radioactive systems because it's basically the same type of process.