Gchem half rxn

[prsndwg]

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Here is the question:

Consider radioactive nuclide X. If 88% of a pure sample decays in 24 hours, what is the half-life?

Why cant I use this equ?

.88/24 = .5/x? I got 16.the answer is 8 from destroyer gchem #187, 2009

I get it when worked backward.. but whats wrong with my way?

 

[Valigator00]

Here is the question:

Consider radioactive nuclide X. If 88% of a pure sample decays in 24 hours, what is the half-life?

Why cant I use this equ?

.88/24 = .5/x? I got 16.the answer is 8 from destroyer gchem #187, 2009

I get it when worked backward.. but whats wrong with my way?

If .88 decayed in 24 hrs, .12 of original sample is left.

so;
1 half life= leaves us with .5 sample left
2nd half life=.25 of sample left
3rd half life=.125 sample left
Sample had to go through three half lives to get to .12 of its original sample. To figure out what the half life is, you divide 3 into 24 to get 8hrs. Hope that helps.

You are not reading the question correctly. Half life does not decrease by a proportional amount, so you can't use ratios. You have to either use the half life formula.