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

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 $t=10 \mathrm{yr} .$ Initially $1.0 \mathrm{mg}$ of ${ }^{238} \mathrm{Pu}$ was present in the pacemaker. (Hint: After $10 \mathrm{yr}$, the activity of the isotope decreases by 8.0 percent. Power is measured in watts or $\mathrm{J} / \mathrm{s}$.

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 $t=10 \mathrm{yr} .$ Initially $1.0 \mathrm{mg}$ of ${ }^{238} \mathrm{Pu}$ was present in the pacemaker. (Hint: After $10 \mathrm{yr}$, the activity of the isotope decreases by 8.0 percent. Power is measured in watts or $\mathrm{J} / \mathrm{s}$.

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.

Transcript

00:01 Consider the radioactive isotopes um plutonium -238 it's used in pacemakers decays by emitting an alpha particle with a half -life of 86 years part one is to write a um excuse me doing two things at once here equation for the decay process so i'll have 238 98 .94 pu and it's emitting an alpha particle.

00:54 So this will give me 234 .92 uranium.

01:00 Okay very good.

01:02 And for step b or part b we're asked to that we're given an energy of the emitted alpha particle is 9 .0 times 10 to the minus 13th joules.

01:32 That is the energy per decay.

01:40 Assume that all the alpha particles used on the pacemaker calculate power output at t0 and at t equals 10 years.

02:05 Initially, we have 1 .0 milligrams of sample.

02:15 We have a hint after 10 years the activity decreases 8 percent.

02:36 Power is measured in watts or joules per second.

02:40 Okay i don't know if i'm going to have enough room to do the next page so i can think so um so let's do our ln of n t over n o the half -life is 0 .3 so our half -life is 86 years okay the number of pu atoms at t0 will be equal to to 1 .0 milligrams times 1000 milligrams per gram times 238 milligrams per mole times avogadro's this will equal 6 .022 times 10 to the 23rd divided by 1 ,000 divided by 238.

04:43 238.

04:44 And this will equal 2 .53 times 10 to the 18th atoms.

04:57 Okay.

04:58 My rate constant will be equal to 0 .693 divided by 86 years...

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