Suppose you want to make a scale model of a hydrogen atom. You choose, for the n

Question

Suppose you want to make a scale model of a hydrogen atom. You choose, for the nucleus, a small ball bearing with a radius of 1.5 mm. The radius of the hydrogen atom is 0.529 × 1010 m and the radius of the nucleus is 1.2 × 1015 m. (a) What would be the radius (m) of the model? (b) Suppose that now you want to make a scale model of the solar system using the same ball bearing as in part (a) to represent the sun. How far from it (mm) would you place a sphere representing the earth? (Center to center distance please.) (See the inside cover of your textbook for data.) (c) What would be the radius (mm) of the sphere representing the earth in part (b)?

Explanation / Answer

Scale = Rb / Rn = 1.5*10^-3 / 1.2*10^-15 = 1.25*10^12

Rm = 1.25*10^12 * 5.29*10^-11 = 66.125 m

b) Rbb = radius of the ball bearing = 1.5 mm = 0.0015 m
Rs = radius of the sun = 6.96 x 10^8 m
Dcc = center to center distance between the earth and the sun = 1.496 x 10^11 m

6.96 x 10^8 m / 0.0015 m = 6.96 x 10^8 m / 1.5 x 10^-3 m = 4.64 x 10^11

The sun's radius is 4.64 x 10^11 times as large as the radius of the ball bearing.

Distance of a sphere representing the earth from the ball bearing (d) =
d = (1.496 x 10^11 m)/(4.64 x 10^11) = 0.322 m

c) Re = radius of the earth = 6,371 km = 6,371,000 m = 6.371 x 10^6 m

Radius of the sphere representing the earth (Rsph) =
Rsph = 6.371 x 10^6 m / 4.64 x 10^11 = 1.373 x 10^-5 m = 0.0000137 m

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