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)