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?
The mass of Uranium halves every 4.5 billion years, so 13.5 billion years= 3 half-lives.
[tex]M=M_{0}[/tex] × [tex](\frac{1}{2} )^n[/tex]
Is the equation that describes the decay, where [tex]M^0[/tex] is the initial mass and [tex]n[/tex] is the number of half-lives passed.
So if 3 half-lives have passed:
[tex]M=M_{0}[/tex] × [tex](\frac{1}{2} )^3[/tex]
[tex]M=M_{0}[/tex] × [tex](\frac{1}{8} )[/tex]
[tex]M= \frac{1}{8} M_{0}[/tex]
So there will be 1/8 of the original mass left after 13.5 billion years, or 12.5% of the mass left.
