Question

The average radius for the planet earth is 3.96 x 103 miles. Given that the atomic weight of aluminum is 26.9815 and the atomic radius is 0.143 nm (nanometers), calculate:

-the length of the line formed in meters if the atoms in 27.2 g of aluminum were placed side by side?

- how many times the line in the question above, would stretch around the Earth?

Answer 1

Because 2698 g of Al contains 6023 times 10^23 atoms Each atoms with diameter (d) = 2r, when placed side by side would form line of length (L) Implies L = 6.023 times 10^23 times 2 times r {where, r = 0.143 (nm)} Implies L = 6.023 times 10^23 times 2 times 0.143 times 10^-9 (m) Implies L = 1.72 times 10^4 m. The line with found length would stretch, (N) times around the Earth where, N = L / 2 Pi r_e (where r_e is the radius of the earth Implies r_e = 3.96 times 103 times 1609.34 m) Implies N = 172 times 10^14 / 2 times Pi times 3.96 times 103 times 1609.34 Implies N = 41765504.59 times