Question

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

Answer 1

Answer: The footprints were made
`2.99* 10^6years` years long ago.

Step-by-step explanation:

Radioactive decay follows first order kinetics.

Half-life of isotope X= 500,000 years

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(500000)=0.00000139year^(-1)`

The equation for first order kinetics is :

`N=N_o* e^(-\lambda t)`

N = amount left after time t = 0.125 mg

`N_0` = initial amount = 8.00 mg

`\lambda` = rate constant

t= time

Putting the values we get:

`0.125=8.00* e^{- 0.00000139years^(-1)* t}`

`0.0156=e^{- 0.00000139years^(-1)* t}`

`t=2.99* 10^6years`

The footprints were made
`2.99* 10^6years` years long ago.