Approximately how long would it take a sample of iodine-131 to lose 99% of its radioactivity? Iodine-131 has a half-life of about 8 days.

Ugh.. Idk why I'm complicating my life with Half lives but I was told they are easy.. yet somehow I have a hard time with them. ):
Someone please help? :/

Question

Approximately how long would it take a sample of iodine-131 to lose 99% of its radioactivity? Iodine-131 has a half-life of about 8 days.

Ugh.. Idk why I'm complicating my life with Half lives but I was told they are easy.. yet somehow I have a hard time with them. ):
Someone please help? :/

kc_kennylau · Answer

does it decay directly into non-radioactive material?

kc_kennylau · Answer

(I think geometric progression is needed here)

anonymous · Answer

if 99% decays that means 1 % is left, which would be .01 * 131 = 1.31.  You divide 131 by 2 continuously until you fall below that number.  131 has to be divide by 2 seven times before it is <1.31.  
That means 7 half lives.  
Each half life is 8 days so 7*8 = 56.  Unless you need the exact decimal which requires more steps

anonymous · Answer

I think so because that's what the whole chapter is about! idk about geometric progression though.. I'm actually not really sure what that is! THANKS for replying btw, you rock!

anonymous · Answer

I'm working on mastering chemistry so it's a bit picky.. I think I will need the exact decimal 
What steps do you mean? And if it's not too much trouble, could you guide me through them or at least let me know what they are? thanks!(:

anonymous · Answer

im a bit confused on what units you need to express time in? in my book im told that time is in secs. but arbitor seems to have gotten it correct with 7 half lifes are required for you to have 1% or less left. but instead of puttting it in days u should convert that into secs.

anonymous · Answer

The unit is in days. Hm.. well he said I would require more steps if I want the exact number which I need because I'm working on mastering chem. :/

aaronq · Answer

This problem is asking how long it will take for 99% of the sample to decay (a first order problem) so you can use $A_t=A_o*e^{\dfrac{-ln2*t}{t_{1/2}}}$ and solve for t.

$0.01=1*e^{\dfrac{-ln2*t}{8~days}}\rightarrow  t=-\dfrac{ln(0.01)*8~days}{ln(2)}=53.1508495181977976 ~days$

anonymous · Answer

I don't ever remember using that formulae in class.. we've only used log but the answer was right. I will research it more. THANK YOU SO MUCH FOR HELP!!(: Aaronq, you're always coming to my rescue! (: Thanks a million!