Question

Measurements indicate that 27.83 % of all rubidium atoms currently on the earth are the radioactive isotope. The rest are the stable isotope. The half-life of is y. Assuming that no rubidium atoms have been formed since, what percentage of rubidium atoms were when our solar system was formed y ago?

Short answer

The percentage of rubidium atoms when our solar system was formed y ago is 29.20 %.

Step-by-step solution

Formulas used to solve the question

Relation between half-life and decay constant

Determine the number of rubidium nuclei

Let the number of nuclei now is N, the number of is N, which is constant and the number of at the beginning is .

So, the total number of rubidium atoms, now, is , and its number at the beginning is .

Currently, only 27.83 % of all rubidium atoms on the earth are the radioactive isotope.

Thus,

Solve for N,

.............(i)

Determine the percentage

Now, the number of rubidium atoms as a percentage when the solar system was formed is,

................(ii)

The number of remaining nuclei is given by,

Solve for substitute it into equation (ii),

Plug the values,

..................(iii)

Here,

And

Now, plug the values in equation (iii),

Thus, the percentage of rubidium atoms when our solar system was formed y ago is 29.20 %.