Uranium-238 decays very slowly with a half life of 4.5 billion years. what percentage of a sample of uranium-238 would remain after 13.5 billion years?

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Answer 1 · 2018-04-25T14:17:41

#(1/8)# or #12.5%# of the mass left.

The mass of Uranium halves every 4.5 billion years, so 13.5 billion years= 3 half-lives.

#M=M_0 times (1/2)^n#

Is the equation that describes the decay, where #M_0# is the initial mass and #n# is the number of half-lives passed.

So if 3 half-lives have passed:

#M=M_0 times (1/2)^3#

#M=M_0 times (1/8)#

#M=(1/8)M_0#

So there will be #(1/8)# of the original mass left after 13.5 billion years, or #12.5%# of the mass left