The calculations are not hard, and it is interesting (and maybe useful?) to be able to visualize these things.
There are many estimates of LD50 for imidacloprid on honey bees, but let's take a published value of 0.008 µg (8 ng) per bee. (
http://www.cdpr.ca.gov/docs/emon/pubs/fatememo/Imidclprdfate2.pdf)
A worker bee weighs about 100 mg. Thus the toxicity of imidacloprid to honey bees is 8 ng/100 mg = 0.08 mg/kg, if we use the same units as LD50 for mammals. This is about 600 times more toxic than nicotine, 80 times more toxic than cyanide, 20 times less toxic than ricin, and 8000 times less toxic than botulinum, the most human-toxic compound known. Not quite snake venom, but at the same time no compound with this level of toxicity to humans would be allowed to be freely dispersed into the environment.
The LD50 of imidacloprid to rats (the best proxy for humans) has been estimated at 450 mg/kg. Thus the chemical is over 5000 times more toxic to bees than it is to us. Of course that level of specificity is desirable in an insecticide, but when your livestock happen to be insects that is a problem.
It's not easy for me to visualize 80,000 hives, so I'll stick with one. One hive with 60,000 bees. Killing half the bees in a hive would thus require 480,000 ng, or 0.48 mg of imidacloprid. Seed corn is treated at rates of 0.25 to 1.25 mg per kernel. (
http://www.extension.iastate.edu/CropNews/2012/0406hodgson.htm) At the higher rate, one kernel contains enough imidacloprid to kill half the bees in two full strength hives. At the lower rate it would take two kernels to kill half the bees in one hive.
This analysis of course ignores the fact that bees are affected at dosages much lower than the LD50, and it makes the assumption that the chemical would somehow be distributed equally to all bees in the hive, which is false. But still, corn is planted at the rate of 35,000 seeds per acre, and one or two seeds contain enough imidacloprid to kill a whole hive. Corn planting is a dusty endeavor, and not all of that imidacloprid stays on the seed. That would be enough to scare me if I kept bees in corn country, or at least convince me to move my hives well away from fields during planting time.
I don't know that we need to ban imidacloprid and its related neonic cousins, but we need to realize that from a bee's perspective we are dispensing a chemical 80 times more toxic than cyanide across wide expanses of ag lands adjacent to hives. We definitely need rules (isolation distances and times) to improve coexistence.
Mark