Gchem- any one knows Exponential decay?!!!

[Ocean5]

Hi every body,
Could come one please help me with exponential Decay? It is just one page on the very last page of kaplan's book. Gchem- lesson 12, very last page. It has a couple of calculations that I don't understand. Also Q number 4 of lesson 12 is asking about exponential decay.
Could anyone explain this to me please . thank you.

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[albodent]

well, you have Z for the atomic mass (protons and neutrons) and A for atomic number (protons and electrons).

for alpha decay, you subtract 4 from Z and 2 from A and you get the new atom. Same as subtracting a [He]

for beta - decay you only add 1 to A.

beta + you subtract 1 from A

gamma you do nothing because everything converts to each other.

 

[Ocean5]

well, you have Z for the atomic mass (protons and neutrons) and A for atomic number (protons and electrons).

for alpha decay, you subtract 4 from Z and 2 from A and you get the new atom. Same as subtracting a [He]

for beta - decay you only add 1 to A.

beta + you subtract 1 from A

gamma you do nothing because everything converts to each other.

Thanks for your post. What you are explaining here is isotope decay. I'm unclear about exponential decay which has some formulas as follows:
Change n/change t=-(something like upsidedown gamma sing)n
and n=n0 e> -(updiedown gamma)n
Please tell me what is going on with this subject.

There is a problem which is asking:
If at time T=0 there is 2 mole sample of radioactive isotopes of decay constatnt 2 (hous)>-1, how many nucleii remain after 45 mins?

 

[PD3]

It sounds like what you are referring to is rate law stuff. I believe nuclear follows first order kinetics.

 

[Ocean5]

It sounds like what you are referring to is rate law stuff. I believe nuclear follows first order kinetics.

The lesson is on nuclear. But I don't think that it is about kinetics, or I don't know. Bc you might be right, but I don't have sufficient knowledge on this part. The title of the section is exponential Decay and it is just a paragraph of explanation that is all. Please let me know if any one know s this by chance.

 

[biocmp]

It is just a rate law on decay. It follows a specific constant, like the problem, says that it is decaying at 2mol/hour. The sign that you are talking about is lambda. Lambda is the rate at which decay is occurring.

So lambda = 2 mol/hour

and we are only allowing our 2 mol sample to decay for 45 minutes.
45 minutes = 3/4 of an hour, so plugging that into the equation
where e is raised to the -(lambda)t, we get:

e raised to - {(2) x 3/4 }

2 x 3/4 = 6/4 = 3/2

so e is raised to the -3/2 and this equal to .22
So this tells us that our initial 2 mole sample has decayed to .22 or 22% of it's original size.

.22 x 2 = .44 mol are left.

and it wants to know how many nuclei are left(this is equal to the number of atoms, because each atom has only one nuclei)

so take .44 and multiply it by 6.022x 10`23 and you get 2.6 x 10`23

I hope that didn't confuse you more.

for reference No = amount of moles you started with, and e raised to the -(lambda x t) is just the decay equation

so, N will equal the amount of material left after you started out with No moles of substance and it decays following e raised to the -(lambda x t) with respect to the amount of time you allow it to decay.

if i made it sound hard, it isn't. it has 3 parts. starting amount (moles), decay constant, and the amount of time you allow it to decay. This all will equal the amount you are left with