Question

Are there any situations in which we
cannot apply Newton's laws of motion?
Is there any alternative for it?​

Answer 1

Newtonian mechanics can only be applied to particles, with specified positions and velocities, interacting with each other by means of forces.

But the Newton's laws of motion don't apply on subatomic particles. It is impossible to assign a specific position and velocity to a subatomic particle. Each particle can be in a superposition of different states. Newtonian mechanics doesn't apply on these subatomic particles

Yes there is alternative to study subatomic particles. We use Quantum Mechanics to measure their properties.

I hope it helps.