A typical home uses approximately 1.0⨉10³ kWh of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?

Video transcript

Hey everyone in this example, we're told that the energy produced from a nuclear reaction is used to power a typical home that uses 2. times 10 to the third power kilowatt hours per month. We need to figure out how much mass and grams is needed to power the home for one year. So what we're going to first recall is because we have our energy and units of kilowatt hours. We want to convert this to jules. So we're going to take our 2.3 times 10 to the third power kilowatt hours. And we're going to convert from kilowatt hours to jewels by recalling the conversion factor that for one kilowatt hour we have 3.6 times 10 to the sixth. Power jewels were now able to cancel our units of kilowatt hours, leaving us with jewels for energy. And this is going to give us an energy value equal to 8. times 10 to the ninth power jewels. Now we want our final answer to be in units of grams. So we should recall that. We can, we should recall the conversion factor where one jewel is equal to one kg times meter squared divided by seconds squared. So we can take this energy value and related to our mass energy equation where we have mass is equal to energy divided by the speed of light squared. And we can say that our energy and our numerator is 8.28 times 10 to the ninth. Power units of kilograms times meters squared divided by seconds squared. In our denominator, we're going to recall that our speed of light is 3.0 times 10 to the eighth. Power meters per second and this is also squared. So now we would be able to cancel our units of squared meters and squared seconds, leaving us with kilograms of their final unit and we would get a value equal to 9.2 times 10 to the negative eighth power kilograms. Now we want to convert from kilograms to grams. So we should recall that for one kg. We have 10 to the third power grams. This allows us to cancel out kilograms Leaving us with grams with our final unit. And what we're going to get here is a result equal to 9. times 10 to the negative fifth power grams. Now we need to calculate this mass for one year. So we're going to take our 9.2 times 10 to the negative fifth power grams. And we're going to assume that this is per month And we're going to recall our conversion factor that we have for 12 months. And sorry, this should say months, that is equivalent to one year. So now we're able to get rid of the units months leaving us with grams per year as our final units. And this will give us our final answer for this example equal to 1.1 times 10 to the negative third power grams. So this here would be our final answer as the mass per year needed to power our home for one year. So I hope that everything I explained was clear. If you have any questions, just leave them down below and I will see everyone in the next practice video.