The half-life of 52^132 Te is 3.26 days. This isotope decays by beta emission to a highly unsta

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The half-life of 52^132 Te is 3.26 days. This isotope...

The half-life of ${ }_{52}^{132} \mathrm{Te}$ is $3.26$ days. This isotope decays by beta emission to a highly unstable intermediate that decays rapidly to a stable product by beta emission. a. What is the ultimate product obtained from Te-132? Write a balanced equation for this reaction. b. Gaseous $\mathrm{H}_{2} \mathrm{Te}$ is made with Te-132. When the tellurium isotope decays, the $\mathrm{H}_{2}$ Te produces $\mathrm{H}_{2}$ and the ultimate decay product of Te-132. Write a balanced equation for the formation of stable products from $\mathrm{H}_{2}{ }^{132}$ Te. c. If a pure sample of $0.0125 \mathrm{~mol}$ of $\mathrm{H}_{2}$ Te made entirely of Te-132 is placed in an evacuated $1.50$ -L flask, how much $\mathrm{H}_{2}$ Te remains after $99.0 \mathrm{~h} ?$ If the temperature is $25^{\circ} \mathrm{C}$, what is the pressure in the flask?

The half-life of ${ }_{52}^{132} \mathrm{Te}$ is $3.26$ days. This isotope decays by beta emission to a highly unstable intermediate that decays rapidly to a stable product by beta emission.
a. What is the ultimate product obtained from Te-132? Write a balanced equation for this reaction.
b. Gaseous $\mathrm{H}_{2} \mathrm{Te}$ is made with Te-132. When the tellurium isotope decays, the $\mathrm{H}_{2}$ Te produces $\mathrm{H}_{2}$ and the ultimate decay product of Te-132. Write a balanced equation for the formation of stable products from $\mathrm{H}_{2}{ }^{132}$ Te.
c. If a pure sample of $0.0125 \mathrm{~mol}$ of $\mathrm{H}_{2}$ Te made entirely of Te-132 is placed in an evacuated $1.50$ -L flask, how much $\mathrm{H}_{2}$ Te remains after $99.0 \mathrm{~h} ?$ If the temperature is $25^{\circ} \mathrm{C}$, what is the pressure in the flask?

Key Concepts

Ideal Gas Law and Stoichiometry

The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas. In the context of nuclear decay that produces gaseous products, this law, along with stoichiometric relationships, is used to calculate properties such as pressure in a confined volume after a decay process.

Balanced Nuclear Equations

Balanced nuclear equations are essential for representing nuclear reactions. They account for the conservation of mass and atomic numbers by ensuring that the sum of the mass numbers and atomic numbers of the reactants equals that of the products.

Exponential Decay and First-Order Kinetics

Exponential decay describes the mathematical behavior of radioactive decay as a first-order process, where the decay rate is proportional to the number of nuclei present. This concept is used to compute the fraction of a radioactive substance remaining after a specific period using its half-life.

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or positron) is emitted. This process results in the transformation of a neutron into a proton (or vice versa), thereby increasing or decreasing the atomic number of the isotope while keeping its mass number constant.

Half-Life

Half-life is a fundamental concept in nuclear chemistry that describes the time required for half of a sample of a radioactive isotope to decay. It is used to calculate the rate of decay and predict the remaining quantity of a radioactive substance over a given period.

Nuclear Decay Chain

A nuclear decay chain is the sequence of decays that a radioactive isotope undergoes until it reaches a stable nuclide. This concept involves understanding intermediate unstable products and how successive decay steps eventually lead to a stable end-product.

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