The radioactive isotope ^238 Pu, used in pacemakers, decays by emitting an alpha particle with a

step 1 Answer for Part A, Pallonium having atomic mass 238 and atomic number 94. Converture to helium t

The radioactive isotope ^238 Pu, used in pacemakers, decays...

The radioactive isotope $^{238} \mathrm{Pu},$ used in pacemakers, decays by emitting an alpha particle with a half-life of 86 yr. (a) Write an equation for the decay process. (b) The energy of the emitted alpha particle is $9.0 \times$ $10^{-13} \mathrm{J},$ which is the energy per decay. Assuming that all the alpha particle energy is used to run the pacemaker, calculate the power output at $t=0$ and $t=10$ yr. Initially $1.0 \mathrm{mg}$ of $^{238} \mathrm{Pu}$ was present in the pacemaker. (Hint: After 10 yr, the activity of the isotope decreases by 8.0 percent. Power is measured in watts or J/s.)

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This decay is spontaneous and occurs at a rate described by an exponential decay law, where the number of undecayed nuclei decreases over time.

Half-Life

The half-life of a radioactive substance is defined as the time required for half of the radioactive nuclei in a sample to decay. It is a constant characteristic of each radioactive isotope and determines the rate at which the material decays.

Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle, consisting of two protons and two neutrons. This process reduces the mass number of the original nucleus by four and is typical in heavy elements.

Radioactive Activity

Radioactive activity is the measure of the rate at which a sample of radioactive material decays, typically expressed in decays per second (becquerels) or in curies. It depends on both the number of radioactive nuclei present and the decay constant related to the half-life.

Power Calculation in Radioactive Decay

Calculating the power output from a radioactive source involves multiplying the activity (number of decays per second) by the energy released per decay. This allows for determining the rate at which energy is produced, providing a direct link between the decay process and practical applications like powering devices.

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