${}^{227}\mathrm{Ac}$ has a half-life of 22 years with respect to radioactive decay . The decay follows two parallel paths : ${}^{227}\mathrm{Ac}\to {}^{227}\mathrm{Th}$ and ${}^{227}\mathrm{Ac}\to {}^{223}\mathrm{Fr}$. If the percentage of the two daughter nuclides are $2.0$ and $98.0$, respectively, the decay constant (in year ${}^{-1}$ ) for ${}^{227}\mathrm{Ac}\to {}^{227}$ Th path is closest to