A radioactive nuclei with decay constant $0.5/\mathrm{s}$ is being produced at a constant rate of 100 nuclei/s. If at $t = 0$ there were no nuclei, the time when there are 50 nuclei is:\\
(1) 1 s\\
(2) $2\ln\left(\frac{4}{3}\right) \mathrm{s}$\\
(3) $\ln 2 \mathrm{~s}$\\
(4) $\ln\left(\frac{4}{3}\right) \mathrm{s}$