Plutonium has a half-life of 8×107 years. How long will it take for 5 g of plutonium todecay into 1 g.

Radioactive decay takes place when an unstable nucleus becomes stable. The instability arises due to…

Answered: Plutonium has a half-life of 8×10¹…

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Plutonium has a half-life of 8×10¹ years. How long will it take for 5 g of plutonium to decay into 1 g.

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Question

Plutonium has a half-life of 8×107 years. How long will it take for 5 g of plutonium to
decay into 1 g.

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.

The radioactive 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.