2. A medical imaging device shoots 8 million electrons per second through an Ohmic gas.
The electrons are
motivated by a 3000 V potential difference. What is the effective resistance of the gas?

That's more than ohms law because we have to convert 8 million electrons per second to a current.

One electron has a charge of  1.602 × 10⁻¹⁹ coulombs so 8 million = 8×10⁶ have a charge of

q = 8×10⁶ × 1.6 × 10⁻¹⁹ = 1.3×10⁻¹²

Since that goes by in one second, that's also the current in amps,

I = 1.3×10⁻¹² amps

That's a tiny current.   If that flowed across 3000 Volts that implies a resistance of

R = V/I = 3000/1.3×10⁻¹² = 2.3 × 10¹⁵ ohms

That's a giant resistance.  

These numbers don't seem all that realistic but I think it's right.

   about 2.34 PΩ

Explanation:

One electron is 1.602176634×10^−19 coulomb, so 8×10^6 electrons per second is ...

  (8×10^6)(1.602176634×10^−19) amperes ≈ 1.28174×10^-12 amperes

Then the resistance is ...

  R = V/I = 3000/(1.28174×10^-12) ≈ 2.34×10^15 . . . ohms

The SI prefix corresponding to 10^15 is "peta-", so this is ...

  2.34 PΩ