At very small length scales (atomic sizes and smaller), classical mechanics must be replaced by:

a. Quantum mechanics

b. Relativistic mechanics

c. Lagrangian mechanics

d. Hamiltonian mechanics

At very small length scales (atomic sizes and smaller), classical mechanics must be replaced by a. Quantum mechanics. Relativistic mechanics has more to do with speed rather than size. In particular, if an object (whether quantum or classical) moves at a speed close to that of light, then relativity takes effect. Lagrangian and Hamiltonian mechanics are both just more advanced versions of classical physics. These methods use calculus instead of just basic mathematics, but these are still classical nonetheless.