If the average household uses electrical energy daily at the rate of 500. W, how much U-235 must undergo fission to supply this need for a year? (assume 200. MeV of energy are generated per fission and that the power plant is 46% efficient).

1. Energy used in Joules per year?

2. Fissions needed per year to produce the energy?

3. Mass of uranium needed to produce the fissions?

To find the answers to these questions, we need to break down the problem into multiple steps. Let's go through the calculations step by step:

Step 1: Calculate the energy used in Joules per year.
Given:
- Average daily electrical energy usage = 500 W
- Number of days in a year = 365

To find the energy used in Joules per day, we can multiply the average daily electrical energy usage by the number of seconds in a day:
Energy per day = 500 W * 24 hours * 60 minutes * 60 seconds

To find the energy used in Joules per year, we multiply the energy per day by the number of days in a year:
Energy per year = Energy per day * 365 days

Step 2: Calculate the number of fissions needed to produce the energy.
Given:
- Energy generated per fission = 200 MeV
- Power plant efficiency = 46%

To convert energy from MeV to Joules, we know that 1 MeV is equal to 1.6 x 10^-13 Joules.

First, we need to calculate the total energy needed per year in Joules. We can multiply the answer from Step 1 by the power plant efficiency to account for the efficiency losses:
Total energy needed per year = Energy per year / Power plant efficiency

Next, we need to calculate the number of fissions needed to produce this energy. We divide the total energy needed per year by the energy generated per fission:
Number of fissions needed per year = Total energy needed per year / Energy generated per fission

Step 3: Calculate the mass of uranium needed to produce the fissions.
To find the mass of uranium needed to produce the fissions, we need to use the fact that the mass of one mole of U-235 is approximately 235 grams.

First, we need to find the number of moles of U-235 needed for the number of fissions calculated in Step 2:
Number of moles of U-235 = Number of fissions needed per year / Avogadro's number

Finally, we can convert the number of moles of U-235 to grams by multiplying by the molar mass of U-235:
Mass of uranium needed = Number of moles of U-235 * Molar mass of U-235 (approximately 235 grams)

By following these steps, you can calculate the answers to the given questions.