How do you calculate the number of days required for 3/4 of a given amount of nuclide to decay if the half-life is 18 point 72 days?

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Answer 1 · 2014-05-29T02:04:40

You calculate the number of half-lives and multiply by the length of one half-life.

The number of half-lives is #n = t/t_(1/2)#, so #t = nt_(1/2)#.

For each half-life, you divide the total amount of the isotope by 2, so

Amount remaining = #"original amount"/2^n# or

#A = A_0/2^n#

You can rearrange this to

#A_0/A = 2^n#

If original amount was 1, and #3/4# of the nuclide decayed, then #1/4# of the nuclide remains undecayed.

#1/(1/4) = 2^n#

4 = #2^n#

#n# = 2

#t = nt_(1/2)# = 2 × 18.72 days = 37.44 days