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 Ã 10â10 m and the radius of the nucleus is 1.2 Ã 10â15 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)?

Answer 1

Answer:

A)  x _electron = 0.66 10² m , B)   x _Eart = 1.13 10² m , C)  d_sphere = 1.37 10⁻² mm

Explanation:

A) Let's use a ball for the nucleus, the electron is at a farther distance the sphere for the electron must be at a distance of

Let's use proportions rule

                x_ electron = 0.529 10⁻¹⁰ /1.2 10⁻¹⁵ 1.5

               x _electron = 0.66 10⁵ mm = 0.66 10² m

B) the radii of the Earth and the sun are

               $R_{E}$ = 6.37 10⁶ m

                tex]R_{Sum}[/tex] = 6.96 10⁸ m

                Distance = 1.5 10¹¹ m

                x_Earth = 1.5 10¹¹ / 6.96 10⁸  1.5

                x _Eart = 1.13 10² m

C) The radius of a sphere that represents the earth, if the sphere that represents the sun is 1.5 mm, let's use another rule of proportions

            d_sphere = 1.5 / 6.96 10⁸  6.37 10⁶

            d_sphere = 1.37 10⁻² mm