radioactive elements, half life and earth

[dg2008]

Question

 

Amongst the radioactive elements that were incorporated when the earth was formed were:

 

uranium 238U with a half-life of 4.5 × 10^9 y

 

uranium 235U with a half-life of 7.1 × 10^8y

 

thorium 230Th with a half-life of 8.0 × 10^4 y

 

iron 60Fe with a half-life of 1.5 × 10^6 y

 

manganese 53Mn with a half-life of 3.6 × 10^6 y

 

thorium 232Th with a half-life of 13.9 × 10^9 y or 1.39 x 10^10

 

Given that the earth is believed to have formed 4600 Ma ago, which of the above could still be contributing to the radioactive heating of it's interior?

 

Answer

 

In that case 4600 Ma = 4.6 x 10^9 y

 

Start by calculating the ratio of what is left, that ratio for what has decayed is 0.5 raised to the power time/half-life.

 

The time being the age of the Earth, so it's the reciprocal of that.

 

So for the first one that's 0.5 to the power (4.6x10^9/4.5 x10^9) or 0.49 take the reciprocal and 51% of the original U238 remains.

 

Am I going in the right direction?

 

I'm thinking that anything below 10^9 can be ignored.

[swansont]

 

I'm thinking that anything below 10^9 can be ignored.

 

What fraction is left after 4.6 half-lives? That will support your answer quantitatively.