External node means leaf.
a binary tree has at most n/2 Leaves. Means at most or order n.
the length of path from root to leaf is at most log(n)
summing over all such nodes gives nlog(n) Lower bound. Option B
this can be always less than order n squared in the worst case. Option A.
option C is not possible because it can be less than that.
Option D is not possible because it is always greater than order n.