A hydrogen atom has a diameter of approximately 1.06 ? 10-10 m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately 2.40 ? 10-15 m

(a) For a scale model, represent the diameter of the hydrogen atom by the length of an American football field (100 yards = 300 ft) and determine the diameter of the nucleus in millimeters.

(b) The atom is how many times larger in volume than its nucleus?

Answer:

a)

hydrogen atom 1.06e-10 m / hydrogen nucleus 2.40e-15 m = 44167 X's as large

100 yards @ 0.9144 metres / yard @ 1000mm/metre = 91,440 millimeter

with the nucleus being 44,167 times smaller:
91,440 mm / 44167 = 2.07mm

answer is: 2.07mm is the diameter of the nucleus in millimeters, if the diameter of the hydrogen atom was 100 yards


(b) The atom is how many times larger in volume than its nucleus

volume = 4/3 pi r^3

volume of the atom @ diameter of 1.06e-10 m = 8.8247e-21m3
volume of the nucleus @ diameter of2.40e-15 m = 4.5239e-30 m3

8.8247e-21m3 / 4.5239e-30 m3 =  1.95e9 times larger