Exponential Growth and Decay Quistion... (1 Viewer)

[+GriM ReApeR+]

The half life of radium is 1600yrs.
a) find the percentage of radium that will be decayed after 500 yrs
b) find the number of years that it will take for 75% of the radium to decay

Thanks

 

[Li0n]

that looks like an MIF question

 

[wogboy]

a) Radium (and other unstable nuclear isotopes) decay at a rate proportional to the amount present.

i.e. dM/dt = -kM (M = mass, k = some positive constant)
-> M = A*e^-kt (when t=0, M=A so you can see the initial amount was A)

when t = 1600 years, M = A/2 (definition of half life)
-> A/2 = A*e^-1600k
->e^-1600k = 1/2
->1600k = ln 2
-> k = ln2/1600

So when t = 500 years,
M = A*e^(-500 * ln2 / 1600)
= 0.815 * A
-> ~ 80.5% remaining
-> ~ 19.5% decayed

b) When we set M = A/4 (three quarters has decayed)
A/4 = A * e^(-kt)
e^(kt) = 4
t = 1/k * ln4
= ln4 / (ln2 / 1600)
= 1600 (ln 4 / ln 2)
= 3200 years

 

[Rorix]

b= 3200 years by inspection

 

[mojako]

b= 3200 years by inspection

oh not again

the HSC markers are supposed to be the inspectors, so if you try to be the inspector yourself they'll get pissed off and won't give you any marks.

 

[Xayma]

Well to put it simply.

Time taken for two half lifes=3200 years.

Two half-lifes=50%+50%(50%)=75% decayed.

 

[Grey Council]

lmao

that inspection thing again

hahahha!!

this is getting ridiculous.
:-\

ND and Wogboy seem good at it. hehe, the biggest and most amazing 'by inspection' I saw was the Archman doing Oldman's clock problem. that was amazing. :-S I still don't get it. humph

oh yeah, the topic of this thread.
hmm
you can find this question in most textbooks, if not all. It's in MiF, fitzpatrick, couchman, and more likely than not, cambridge.

they usually don't ask you this sort though. hmm

 

[mojako]

they usually don't ask you this sort though. hmm

by a quick inspection of the question (without looking at solutions by other posters and without actually doing the question myself),
why not?
I've seen half life question so maybe you just have to understand what half life is.

 

[Xayma]

But it is rare for them to ask you something which involves the half life. Eg How long till 87.5% is decayed, or how much will remain after 4800yrs.

 

[Rorix]

Well to put it simply.

Time taken for two half lifes=3200 years.

Two half-lifes=50%+50%(50%)=75% decayed.

That's my by inspection method