Question

The ceramic glaze on a red-orange Fiestaware plate is U2⁢O3 and contains 50.0 grams of 238U , but very little 235U.

a) What is the activity of the plate?
b) Calculate the total energy that will be released by the 238U decay.
c) If energy is worth 12.0 cents per kW⋅h, what is the monetary value of the energy emitted? (These plates went out of production some 30 years ago, but are still available as collectibles.)

Answer 1

The activity of the Fiestaware plate can be calculated through the decay rate formula, the total energy can be determined using the energy per decay of 238U and the total number of decays, then the monetary value is found by converting the energy to kilowatt hours and applying the given energy cost.

Step-by-step explanation:

To calculate the activity of the 50.0 grams of 238U in the Fiestaware plate, we can use the decay law, which requires the half-life of 238U and the number of moles of 238U present in the plate.

The half-life of 238U is approximately 4.468 billion years, and the molar mass of 238U is 238 grams/mol. To find the total energy released by 238U decay, we use the fact that each decay releases an average of 4.27 MeV of energy, which can be converted to joules (1 eV = 1.602 x 10-19 J).

Finally, to calculate the monetary value of the released energy, we convert the energy from joules to kilowatt hours and multiply by the monetary value of 12.0 cents per kWh.