[32bitkid]

serious question: does nuclear radiation scale linearly with explosive yield?

That question aside, the destructive power of a explosive does not scale linearly with yield [1]

> This relation arises from the fact that the destructive power of a bomb does not vary linearly with the yield. The volume the weapon's energy spreads into varies as the cube of the distance, but the destroyed area varies at the square of the distance.

The destructive effects of one big 5000-megaton bomb is very different than 10,000 half-megaton bombs. Or even worse, 40,000 125-kiloton bombs.

[1] http://www.atomicarchive.com/Effects/effects1.shtml

[arethuza]

The design of particular bombs also plays a part - in most H-bomb designs the bulk of the energy produced comes from the fission of the tamper round the secondary by neutrons produced by the fusion reaction in the secondary.

If a non-fissioning tamper is used then a relatively clean explosion happens (e.g. the Tsar-bomb) - if depleted or enriched uranium is used as a tamper then weapons will be much messier. Indeed some weapon designs explicitly came in "clean" and "messy" versions (the latter often with greater yield) e.g. the US B53:

http://en.wikipedia.org/wiki/B53_nuclear_bomb

Also there is an option of deliberately including a material in a bomb design that will be activated by the neutron flux from the secondary (e.g. cobalt or gold)- so called "salted bombs":

http://en.wikipedia.org/wiki/Salted_bomb

[Ntrails]

We also, historically, tend to test in ways that limit damage. We doubtless have enough weapons to eliminate 95% + of the global population if that were the intent.

[InclinedPlane]

Actually, only underground tests truly limit damage. There are three destructive effects from a bomb. The explosion itself, the fission products from the bomb, and the radioisotopes bred from high neutron flux impacting surrounding materials.

Tests are conducted away from civilization, which lowers the impact of all forms of damage. However, the above ground tests were conducted generally on the surface with only a few exceptions, which would have increased the amount of radioactive fallout due to neutron activation. In contrast, actual use of a nuclear weapon would be in air bursts which would generate very little activated fallout.

Also, the total number and yield of nuclear weapons now in all arsenals would probably not be sufficient to kill even 50% of the world's population. Much of the world lives in high density areas, but much does not. The total area that the world's population lives on is extremely large and only a small percentage of it could be destroyed through nuclear weapons. Though the industrial and economic collapse would lead to massive starvation which would cause even more delayed deaths, but it's difficult to estimate such things.