A hydrogen nucleus has a radius of 1 times 10^-15 m and the electron Is about 5.

Question

A hydrogen nucleus has a radius of 1 times 10^-15 m and the electron Is about 5.3 times 10^-11 m from the nucleus. Assume the hydrogen atom is a ball with a radius of about 5.3 times 10^-11 m and the nucleus is a ball with a radius of 1 times 10^-15 m. 1) What is the volume of the atom? V_atom = 2) What is the volume of the nucleus? V_nucleus = 3) What percentage of the atom is occupied by the nucleus? %_nucleus = 4) How much work (in electron volts) must be performed by an external force to bring in another proton (from very far away) to the "surface" of the nucleus? (Ignore the effects of the electron.) W =

Explanation / Answer

1) Volume of sphere of radius r, V = 4 pi r^3 / 3

Vatom = (4 x pi x (5.3 x 10^-11)^3 ) / 3

Vatom = 6.236 x 10^-31 m^3

2) Vn = (4 x pi x (1 x 10^-15)^3 ) / 3

Vn = 4.189 x 10^-45 m^3

3) Vn/Vatom x 100 = (4.189 x 10^-45)/(6.236 x 10^-31) x 100

= 6.717 x 10^-13

4) at far away , PE of proton = 0

when at the surafce of nucleus, PE = kq1q2 / d

k = 1 / 4 pi e0 = 9 x 10^9

q1 = 1.6 x 10^-19

PE = (9 x 10^9 x 1.6 x 10^-19 x 1.6 x 10^-19 ) / (1 x 10^-15)

PE = 2.304 x 10^-13 J

Work done = change in PE = 2.304 x 10^-13 J

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