52^106 Te is radioactive; it alpha decays to 50^102 Sn · 50^102 Sn is itself radioactive and h

step 1 Solving this problem so I can write for 10652 t late half time half life is equal to t1 by 2 the

52^106 Te is radioactive; it alpha decays to 50^102 Sn ·...

${ }_{52}^{106} \mathrm{Te}$ is radioactive; it alpha decays to ${ }_{50}^{102} \mathrm{Sn} \cdot{ }_{50}^{102} \mathrm{Sn}$ is itself radioactive and has a half-life of $4.5$ s. At $t=0$, a sample contains $4.00 \mathrm{~mol}$ of ${ }_{52}^{106} \mathrm{Te}$ and $1.50 \mathrm{~mol}$ of ${ }_{50}^{102}$ Sn. At $t=25 \mu \mathrm{s}$, the sample contains $3.00 \mathrm{~mol}$ of ${ }_{52}^{106} \mathrm{Te}$ and $2.50 \mathrm{~mol}$ of ${ }_{50}^{102} \mathrm{Sn}$. How much ${ }_{50}^{102} \mathrm{Sn}$ will there be at $t=50 \mu \mathrm{s}$ ?

${ }_{52}^{106} \mathrm{Te}$ is radioactive; it alpha decays to ${ }_{50}^{102} \mathrm{Sn} \cdot{ }_{50}^{102} \mathrm{Sn}$ is
itself radioactive and has a half-life of $4.5$ s. At $t=0$, a sample contains $4.00 \mathrm{~mol}$ of ${ }_{52}^{106} \mathrm{Te}$ and $1.50 \mathrm{~mol}$ of ${ }_{50}^{102}$ Sn. At $t=25 \mu \mathrm{s}$, the sample contains $3.00 \mathrm{~mol}$ of ${ }_{52}^{106} \mathrm{Te}$ and $2.50 \mathrm{~mol}$ of ${ }_{50}^{102} \mathrm{Sn}$. How much ${ }_{50}^{102} \mathrm{Sn}$ will there
be at $t=50 \mu \mathrm{s}$ ?

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This process changes the identity of the element or isotope and is governed by probabilistic laws, making it a key concept in nuclear physics and various applications such as radiometric dating and nuclear medicine.

Exponential Decay

Exponential decay refers to the mathematical description of a quantity that decreases at a rate proportional to its current value, which is characteristic of many first?order processes including radioactive decay. This concept underlies the mathematical modeling of decay processes and is essential for predicting the remaining quantity of a decaying substance over time.

Half-Life

The half-life of a radioactive substance is the time required for half of the original amount of unstable nuclei to decay. It is a fundamental parameter in the study of nuclear decay, facilitating the quantification of decay processes and allowing scientists to compare the stability of different isotopes.

Decay Chain

A decay chain involves a series of successive radioactive decays where the daughter nucleus produced in one decay may itself be radioactive and decay further. Understanding decay chains is important for accurately modeling the behavior of systems where multiple, sequential nuclear transformations occur over time.

First-Order Kinetics

First-order kinetics describes processes, including many radioactive decays, where the decay rate is directly proportional to the number of unstable nuclei present. This concept is central to deriving the exponential decay law and is used to formulate differential equations that predict the evolution of both parent and daughter nuclide quantities over time.

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