How long is one second?

Usain Bolt is a Jamaican sprinter who holds the world record for the $100$ meters of $9.58$ seconds, which is the highest since the start of fully automatic time measurements. The second (symbol: s) is the base unit of time in the International System of Units (SI) and is also a unit of time in other systems of measurement (abbreviated s or sec); it is the second division of the hour by sixty, the first division by $60$ being the minute. What has been the definition of the second since $1967$ by the International System of Units?

a) $\frac{1}{86,400}$ of a mean solar day

b) The duration of $9,192,631,770$ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium $133$ atom

c) The fraction $\frac{1}{31,556,925.9747}$ of the tropical year for $1900$ January $0$ at $12$ hours ephemeris time

d) Half of the period of a pendulum with a length of $39.1$ inches ( $0.994$ m)