A sample has a T1 of 1.0 seconds. If the net magnetization is set equal to zero, how long will it take for the net magnetization to recover to 98% of its equilibrium value?

Given: T1 = 1.0s

The relationship between the equilibrium net magnetization, Mo, and the net magnetization, Mz(t), at time t is:

Mz(t) = Mo(1 - e-t/T1).

When Mz(t) / M0 = 98%:

0.98 = Mz(t) / M0 = (1 - e-t/T1)
0.98 = 1 - e-t/T1
1 - 0.98 = e-t/T1
ln( 0.02 ) = -t/T1
-T1 * ln( 0,02 ) = t
-1.0s * ln( 0,02 ) = 3.9s = t