Question

A radioactive nucleus has a half-life of 5 x 108 years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?

Answer 1

Answer:

So the present mass will be 0.0017002 times of the initial mass of the sample.

Explanation:

Given:

• half life of the given sample, $t'=5\times 10^8\ yrs$

• We know that solar system came in to existence approximately $4.6\times 10^{9}$ years ago.

Let the initial quantity on the formation of the solar system be, $m_o$

Then the final quantity at present be:

$m=m_o\times (\frac{1}{2})^{(t/t')}$

$m=m_o\times (\frac{1}{2} )^{4.6\times 10^9\div(5\times 10^8)}$

$m=m_o\times 0.0017002$

So the present mass will be 0.0017002 times of the initial mass of the sample.