If 1/32 of a parent material is left, compared to 31/32 of daughter, and the half-life is 50,000 years, then how old is the sample?
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251449 years

Explanation:

We can obtain the age of the sample by using the formula;

t1/2 = t ln2/ln(No/Nt)

Where;

t1/2 = half life = 50,000 years

t= elapsed time = the unknown

No = amount of radioactive material originally present

Nt= amount of radioactive material after time (t)

Note;

Since Nt/ No = 1/32

Then No/Nt= 32/1

Substituting values

t= t1/2 ln(No/Nt)/ln 2

t= 50000 × ln(32/1)/ln 2

t= 50000 × 3.47/0.69

t= 251449 years

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