Question

A sample of radium-226 will decay to ¼ of its original amount after 3200 years. What is the half-life of radium-226?

years?

Answer 1

Half life is 3200/2

The answer is 1600 years

Answer 2

We have a formula for decay is:

`y=ab^x`

We have given that decay of 1/4 that means y becomes a/4

and time is given 3200 years.

Substituting the values we get:

`(a)/(4)=a(b)^3200`

`\Rightarrow ((1)/(4))^(1)/(3200)=b`

`b=.9995`

Now, we have to find when y becomes a/2 we get:

`(a)/(2)=a((1)/(4))^(1)/(3200))^x`

`\Rightarrow log((1)/(2))=(x)/(3200)log((1)/(4))`

`\Rightarrow 3200\cdot (log2)/(log4)=x`

`\Rightarrow x=1600`

Hence, the half life would be 1600