Question

what is the smallest unit of time

Answer 1

The smallest viable measurement of time is derived from a unit of distance called the Planck length.

Answer 2

Scientific time units. The jiffy is the amount of time light takes to travel one fermi (about the size of a nucleon) in a vacuum. Planck time is the time light takes to travel one Planck length. Theoretically, this is the smallest time measurement that will ever be possible.