Answered: An 1 g sample of a radioactive element…

An 1 g sample of a radioactive element takes 83.92 million years to reduce into 1 µg. Calculate the half-life and identify the element.

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Question

An 1 g sample of a radioactive element takes 83.92 million years to reduce into 1 µg.
Calculate the half-life and identify the element.

Expert Solution

Concept and Principle:

Radioactive decay takes place when an unstable nucleus becomes stable. The instability arises due to a mismatch between the number of neutrons and protons. Only a few configurations of neutrons and protons are stable.

This decay will be exponential in nature and is given by,

$N = N_{0} e^{- 0 .693 (\frac{t}{t_{\frac{1}{2}}})}$

Here N₀ is the original number of radioactive nuclei present, t is the time, and t_1/2 is the half-life of the radioactive sample. This is known as the exponential law of radioactive decay.