Question

The following table shows the currently accepted half-life values for four parent isotopes.

Parent Isotope Currently Accepted Half-Life Values
Uranium-238 4.5 billion years
Uranium-235 704 million years
Thorium-232 14.0 billion years
Rubidium-87 48.8 billion years
Potassium-40 1.25 billion years
Samarium-147 106 billion years

Earth is approximately 4.5 billion years old. Given this information and the data in the table, which of the following isotopes could today contain less than 50 percent of its parent isotope?
Rubidium-87
Thorium-232
Uranium-235
Uranium-238

Answer 1

ok the answers are simple:

Parent Isotope Currently Accepted Half-Life Values: is the first one uranium-238 4.5 billion years

Earth is approximately 4.5 billion years old. Given this information and the data in the table, which of the following isotopes could today contain less than 50 percent of its parent isotope: uranium- 238

Answer 2

The amount of substance present in a certain sample can be calculated through the equation,

A(t) = A(o)(0.5)^(t/h)

where At is the amount now, Ao is the original amount, t is the number of years and h is the half-life.

For a substance to at most 50% of the original amount, we get the half-life value.

At/Ao = 0.5 = 0.5^(4.5/h)

h = 4.5 billion.