Answer:
the decay of half of the nuclei only a half-life has passed , b) in rock time it is 1 108 years
Explanation:
The radioactive decay is given by
N = N₀ [tex]e^{\lambda t}[/tex]
If half of the atoms have decayed
½ N₀ = N₀ [tex]e^{\lambda t}[/tex]
½ = [tex]e^{\lambda t}[/tex] ₀
Ln 0.5 = - λ t
t = - ln 0.5 /λ
The definition of average life time is
[tex]T_{1/2}[/tex]= ln 2 / λ
λ = ln 2 / [tex]T_{1/2}[/tex]
λ = 0.693 / 100 10⁶
λ = 0.693 10⁻⁸ years
We replace
t = -ln 0.5 / 0.693 10⁻⁸
t = 10⁸ years
We see that for the decay of half of the nuclei only a half-life has passed
b) in rock time it is 1 108 years
