The following table shows the currently accepted half-life values for six 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? Potassium-40 Rubidium-87 Samarium-147 Uranium-238

Question

Chemistry

Gael Randolph

28 September, 08:46

The following table shows the currently accepted half-life values for six 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? Potassium-40 Rubidium-87 Samarium-147 Uranium-238

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Santino Aguirre · Answer 1

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.

All values below 4.5 billion as half-life are accepted. From the given list, the substances that would be less than 50% now are:

Uranium - 238; Uranium - 235 and; Postassium-40