Which of the following is the correct relationship of half-life T\({}{1/2}\) and mean life \(\tau\)[tau] of an unstable particle, if \(\lambda\)[lambda] is the decay constant?

W) T\({}{1/2}\) = \(\lambda\tau\)[Half-life equals lambda over tau]

X) T\({}{1/2}\) = \(\tau\)/\(\lambda\)[Half-life equals tau over lambda]

Y) T\({}{1/2}\) = \(\tau\) log\({}{2}\)e [Half-life equals tau log base 2 of e]

Z) T\({}{1/2}\) = \(\tau\) ln (Half-life equals tau natural log of 2]
Z) T\({}{1/2}\) = \(\tau\) ln (2)