Radioactive isotope X has a half-life of 500,000 years. This isotope may be found in some types of volcanic rocks. A particular sample of volcanic rock taken from a layer that covered up some of the earliest known human-like footprints contains 0.125 mg of isotope X. The volcanic rock sample originally contained 8.00 mg of isotope X. How long ago were these footprints made. I need the equation. Thanks. please I am stuck on this question. PLEASE

Answers

Answer 1

Answer: The footprints were made [tex]2.99\times 10^6years[/tex] years long ago.

Explanation:

Radioactive decay follows first order kinetics.

Half-life of isotope X= 500,000 years

[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{500000}=0.00000139year^{-1}[/tex]

The equation for first order kinetics is :

[tex]N=N_o\times e^{-\lambda t}[/tex]

N = amount left after time t  = 0.125 mg

[tex]N_0[/tex] = initial amount  = 8.00 mg

[tex]\lambda[/tex] = rate constant

t= time  

Putting the values we get:

[tex]0.125=8.00\times e^{- 0.00000139years^{-1}\times t}[/tex]

[tex]0.0156=e^{- 0.00000139years^{-1}\times t}[/tex]

[tex]t=2.99\times 10^6years[/tex]

The footprints were made [tex]2.99\times 10^6years[/tex] years long ago.


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I'm also in chemistry.

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Answers

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