Question

Suppose the isotope your skittles® represented was uranium-238 and the trials represent the number of half-lives. how old was the sample at the end of your tests? use table 1 in the introduction to help you answer this question. include your calculations. 3. if 1/8 of a radioactive element remains after 600 years, what is that element's half-life? 4. identify and describe similarities and differences between this experiment and radioactive decay in nature.

Answer 1

I can't answer the first and the last question because no given data is provided. However, I can answer the second question.

if 1/8 of a radioactive element remains after 600 years, what is that element's half-life? 

The formula for half life, t1/2, is:
t1/2 = ln2/K

So we must determine K first. The formula for that is:
A = A₀e^(-kt)
where
A = 1/8*A₀
t = 600 years
Thus,
1/8*A₀ = A₀e^(-k*600)
1/8 = e^(-600k)
Solving for k,
K = 3.466×10⁻³

Therefore,
t1/2 = ln2/3.466×10⁻³ = 200 years