Answer:
3.85 nm
Explanation:
The volume of a sphere is:
V = 4/3 * π * r^3
The volume of a shell is the volume of the big sphere minus the volume of the small sphere
Vs = 4/3 * π * r2^3 - 4/3 * π * r1^3
Vs = 4/3 * π * (r2^3 - r1^3)
If the difference between the radii is 1 nm
r2 = r1 + 1 nm
Vs = 4/3 * π * ((r1 + 1)^3 - r1^3)
Vs = 4/3 * π * ((r1 + 1)^3 - r1^3)
Vs = 4/3 * π * (r1^3 + 3*r1^2 + 3*r1 + 1 - r1^3)
Vs = 4/3 * π * (3*r1^2 + 3*r1 + 1)
The volme of the shell is equall to the volume of the inner shell:
4/3 * π * (r1^3) = 4/3 * π * (3*r1^2 + 3*r1 + 1)
r1^3 = 3*r1^2 + 3*r1 + 1
0 = -r1^3 + 3*r1^2 + 3*r1 + 1
Solving this equation electronically:
r1 = 3.85 nm