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b) Uranium 238 has a half-life of about 4.5 billion years. All the 238 U now on Earth was created a in stars and has been here since the formation of Earth about 4.5 billion years ago. Consider a kilogram of pure 238 U present at the formation of the Earth. i) Calculate the activity of the kilogram at that time. Sketch a graph of the activity of the uranium since then to the present day. Label the axes with appropriate numbers and units. Mark on your graph the half-life and the characteristic decay time. ii) 238U decays through a chain of thirteen very short-lived radionuclides (longest half- live only 1600 years) before reaching a stable isotope of lead. If what remains of this uranium has for the last few million years been in a stable rock formation from which nothing escapes, approximately what activity will the rock have now?