An atom has a diameter of 5.00 Å and the nucleus of that atom has a diameter of 3.00 × 10 − 5 Å . Assume the atom and the nucleus are a sphere.

Question

1.  Determine the fraction of the volume of the atom that is taken up by the nucleus.
2. fraction of atomic volume:
3. Calculate the density of a proton, given that the mass of a proton is  and the diameter of a proton is .
4. density:

Answer 1

I will explain how to solve this, but YOU do the work.

(1)

d_a = diameter of atom

V_a = volume of atom

d_n = diameter of nucleus

V_n = volume of nucleus

V_n/V_a = (4/3)π(d_n/2)³ / [(4/3)π(d_a/2)³] = (d_n/d_a)³

You know d_a and d_n. Plug in the numbers.

(2)

density = mass / volume

d_p = diameter of proton

V = (4/3)π(d_p/2)³

You know d_p. Compute the volume, then divide the mass by the volume. In the given units, the answer will be in amu/(AU)³.