10 (5 points). Dumbledorium, a very rare element, is found in trace quantities i

Question

10 (5 points). Dumbledorium, a very rare element, is found in trace quantities in broomsticks used in Quidditch (sports) matches at Hogwarts Academy of Witchcraft and Wizardry (schoo). The element has two naturally occurring isotopes, Dumbledorium-288 (exact m = 287.894 g/mol) and Dumbledorium-291 (exact mass = 290.948 g/mol). What are the isotopic abundances of both Dumbledorium-288 and Dumbledorium-291 respectively? Use the average atomic weight of 288.746 g/mol for Dumbledorium in your calculations. Having learned to name the elements, what is the most logical chemical symbol for Dumbledorium?

Explanation / Answer

average atomicmass = (288-dumbledorium mass*percentage + 291-dumbledorium mass*percentage)/100

288-dumbledorium percentage = x

291-dumbledorium percentage = 100-x

average atomicmass = 288.746 g/mol

288.746 = ((287.894*x)+(290.948*(100-x)))/100

x = 72

288-dumbledorium percentage = x = 72%

291-dumbledorium percentage = 100-x

                              = 100-72
                  = 28%

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