Question

The half life of titanium 44 is 60 years. If you start with 600 grams, how much will be left after 180 years

Answer 1

`75\ \text{g}`

Step-by-step explanation:

t = Time = 180 years

`t_(1/2)` = Half-life of titanium = 60 years

`N_0` = Initial amount of titanium = 600 g

We have the relation

`N=N_0e^(-\lambda t)\\\Rightarrow N=N_0e^{-(\ln 2)/(t_(1/2))t}\\\Rightarrow N=600e^{-(\ln 2)/(60)* 180}\\\Rightarrow N=75\ \text{g}`

The mass that is left after 180 years is
`75\ \text{g}`.