n = 15. A Bohr orbit with n = 15 comes closest to having a 24 nm diameter .
The formula for the radius r of the nth orbital of a hydrogen atom is
r = n^2·a
where
a = the Bohr radius = 0.0529 nm
We can solve this equation to get
n = √ (r/a)
If d = 24 nm, r = 12 nm.
∴ n = √(12 nm/0.0529 nm) = √227 = 15.1
n must be an integer, so n = 15.