The idiot's guide to: Radioactivity and Nuclear Energy (Pt 2)

Explaining the mathematics behind the model of radioactive decay.
Indefinite integration: http://simple.wikipedia.org/wiki/Antiderivative
Exponential Function: http://simple.wikipedia.org/wiki/Exponential_function

Category:

Education

Tags:

• idiots
• guide
• to
• radiactive
• decay
• nuclear
• energy
• radiometric
• dating
• radioactivity

[JRChadwick]

Lol, I spend the day tutoring mathematics and this is what I come home to watch?

[ThetaOmega]

I'm fairly sure the mathematics is sound, but sod's law says that there's some colossal mistake in there somewhere. If you (or anyone) finds a mistake in the maths, alert me and I shall correct it.

[FelleAndersson]

Why is part 2 always up before part 1? :( Anyways, gonna watch it when part 1 is finished processing ^^

[ThetaOmega]

Nah, part 1 was uploaded months ago, I just needed a refresher in differential equations before I did part 2

[graceman25]

we arent saying that you little liar. we obviously understand it beter than you do. what was the 1st thing you said about this principle. Decay is proportionate to the amount of the substance being measured. Its also proportionate to the substances touching it that it is emitting into. the dating doesnt work because we dont know how much of each substance we have. you are incorrect and we obviously understand this science much better than you. it seems you are the one with the agenda.

[graceman25]

Liar.

The math may be solid, but the variables arent.

fuck off.

[TheStringtheorysucks]

@calvinhobbesliker2

lambda is a constant, not a variable , so it can be taken outside of the integral:

int ( lambda) dt  = (lambda) int dt = lambda * t + c, where c is a constant of integration . This is called an indefinite integral. Applying limits on the integral removes the c. Hope that helps

[brode17]

I have just finished reading an exellent book "why does E=mc^2" by brian cox and jeff forshaw. And like this video it attempts to address high tech disaplines, like theoretical physics and quantum mechanics in "laymans terms".

I myself was able to understand most of what the Brian and jeff where trying to address. But i came to one conclusion. It is pretty dam difficult to make an "Idiots guide" on something as high tech as that...and that includes the mathmatics behind radioactive decay :)

[Akatam0t0ma]

So, been a while and I see there is still no follow up video... :-(

Still, thank you very much for explaining these(Though it will take me a lot more than that to understand radiometric dating properly, lol!).

[thegranitehammer]

Damn, you're ~19 and you know calculus and differential equations. I weep for how much I didn't learn in public school.

[diomedes39]

lamda is a constant and can be moved outside the integral

[nilsandrae]

Note: The decay constant has the inverse dimension of the halftime. So in your example lambda = 0.14a^-1 or 0.14 per year. This is very important when calculating decay.

Like ThetaOmega mentions at 2:17 (in this movie) the number of these atoms left at time t=5a (a=years) with N(t=0)=100 are:

N(5) = 100*e^(-lambda*5) = 100*e^(-ln2/5*5) = 100*e^(-ln2) = 100 * 1/2 = 50 atoms

Usually N are very large numbers, but this is just a exercise in calculus and diff.ecuations. :-)

[nilsandrae]

Things to keep in mind:

dN/dt is the derivative of the amount of atoms N with respect to time t. That is the decay of N atoms at a given time t.

dN/dt is defined as the 'limit' of (N(t+h)-N(t))/h when h->0

and is not the "number of atoms decayed divided by the amount of time passed". This IS a bit confusing at the begining, I know. 'Differentials' like dN and dt can NOT be handled like normal variables in algebra.

[calvinhobbesliker2]

thanks!can you also explain to me what I did wrong:LN 2 is approximately 0.693. if an isotope has a half-life of 5 years, then the decay constant should be approximately 0.14. dN/dt means number of atoms decayed divided by the amount of time passed, right? so if we start with 100 atoms, N would be 100. if we plug 5 years into dt, then we have the following: dN/5 = -0.14(100). 100x-0.14 is -14. so we have dN/5 = -14, and therefore, dN=-70. but since the half-life is 5 years, shouldn't Dn be -50?