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You are a director of your hometown Science Center. For a new display you want to build a scale model of a uranium nucleus, (uranium-238), by densely packing billiard balls representing the individual nucleons.

(a) if you use red balls for the protons and white balls for the neutrons, how many of each will you need?

(b) if each billiard ball has a diameter of 5 cm, approximately how many cm in diameter will be completed model? Hint: No unit conversion needed. But first derive a general formula for the diameter of the nucleus (call it D) as a function of the diameter of a nucleon (call that d).

(c) In reality, will the diameter of the completed model be somewhat larger or somewhat smaller than the value you just calculated in part (b)? Justify your answer. Hint: think geometry! If you are an aficionado, after the end of the class look up “sphere packing” on the internet.

 

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