Question

The half-life of uranium-328 is about 4.5 billion years. After four half-lives have passed, what fraction of the original sample will be left?

Answer 1

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.

`M=M_(0)` ×
`((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)` ×
`((1)/(2) )^3`

`M=M_(0)` ×
`((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.