Question

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after 200 years.

Answer 1

To solve this we are going to use the half life equation
`N(t)=N_(0) e^{( (-0.693t)/(t _(1/2) )) }`
Where:

`N_(0)` is the initial sample

`t` is the time in years

`t_(1/2)` is the half life of the substance

`N(t)` is the remainder quantity after
`t` years

From the problem we know that:

`N_(0) =100`

`t=200`

`t_(1/2) =1600`

Lets replace those values in our equation to find
`N(t)`:

`N(200) =100e^{( ((-0.693)(200))/(1600)) }`

`N(200)=100e^{( (-138.6)/(1600) )}`

`N(200)=100e^(-0.086625)`

`N(200)=91.7`

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.