Second

The second ($\mathrm{s}$) is the SI base unit for time.

It is defined using the caesium-133 hyperfine transition frequency $\Delta {\nu }_{Cs}$. The SI fixes this frequency exactly as:

$$\Delta {\nu }_{Cs}=9192631770\mathrm{Hz}=9192631770{\mathrm{s}}^{-1}$$

So one second is the duration of $9,192,631,770$ periods of the radiation corresponding to that atomic transition.

Why this works: caesium-133 atoms have very stable energy level differences. The relevant transition is between two hyperfine states of the ground state. When radiation has exactly the matching frequency, the atom can absorb it. Atomic clocks tune microwave radiation to this transition and count oscillations.

The associated photon energy is tiny but precise:

$$E=hf$$

with

$$h=6.62607015\times 10^{-34}\mathrm{J}\mathrm{s}$$

so

$$E\approx 6.09\times 10^{-24}\mathrm{J}\approx 38\mu \mathrm{eV}$$

Important unit link: $1\mathrm{Hz}=1{\mathrm{s}}^{-1}$. Frequency is “per second”, so time and frequency are reciprocal. This is why the Metre can be defined from the speed of light once the second is fixed.

Quick check: periods and frequencies invert: $T=1/f$. A higher frequency means a shorter time per cycle.

Quick check

Seconds appear in rates and accelerations. Velocity has one power of time in the denominator,

$$\mathrm{m}{\mathrm{s}}^{-1},$$

while acceleration has two:

$$\mathrm{m}{\mathrm{s}}^{-2}.$$

That second power means acceleration is “change of velocity per second”, not just fast motion.