Joe Bruin learns that the element potassium is radioactive, so he decides he would like to try to heat his new home using the heat generated by radioactive potassium decay. His plan is to dig an underground pit that is square in cross section before his new home is built, and fill it with potassium chloride salt (KCl), which is rich in potassium. The pit will need be 20 meters on a side to cover the footprint of Joe’s new house, and Joe plans to use thermal insulation on all sides of the pit except at the top to ensure that all the radioactive heat generated inside the pit flows into his home. The annual average space heating needs for Joe's house is 4.38 x 10^ 6 W. Based on the above information:

Estimate the mass of KCl that Joe would need to acquire to supply his heating needs. The radioactive isotope of potassium is 40K, which has a natural abundance of 0.012% and has a half-life of 1.248x109 years. Assume that the decay of a 40K atom results in the production 1.3 MeV of heat energy.

Given the mass of KCl that you calculate in Part b., estimate how deep Joe’s potassium pit would need to be, given that the density of KCl is 1.98g cm-3

Joe realizes that using regular potassium chloride to heat his home is not going to work, so he decides to buy a centrifuge and separate all the radioactive 40K atoms to produce pure 40KCl salt. Assuming he could do this, how deep would Joe’s potassium pit then need to be to produce enough heat to heat Joe’s home?