The radioactive isotope 3° Ra has a half life of 1599 years. After 1000 years there is 3.5 grams of the radio isotope present. Approximately how will be present in 10000 years? Assume the material experiences exponential decay.

The radioactive isotope 3° Ra has a half life of 1599 years. After 1000 years there is 3.5 grams of the radio isotope present. Approximately how will be present in 10000 years? Assume the material experiences exponential decay.

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Question

2. The radioactive isotope 236 Ra has a half life of 1599 years. After 1000 years there is 3.5 grams of
the radio isotope present. Approximately how will be present in 10000 years? Assume the
material experiences exponential decay.

Expert Solution

Step 1

Radioactive Decay Law

The rate of decrease in the number of radioactive nuclei is directly proportional to the instantaneous number of radioactive nuclei.

$\frac{d N}{d t} = - λ N$

$λ$ is a constant and is known as the decay constant of the material. Thus the solution of this differential equation is

$N = N_{o} e^{- λ t}$

$N_{o}$ is the integration constant and is the number of radioactive nuclei at the initial time. This equation gives the number of radioactive nuclei left as a function of time.

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