The decay constant
\(k\, = \,\frac{{0.693}}{{{t_{1/2}}}}\, = \,\frac{{0.693}}{{10\,\,days}}\, = \,0.0693\,\,day{s^{ - 1}}\)
The time required for one fourth conversion
\(t\, = \,\frac{{2.303}}{k}\,{\log _{10}}\frac{a}{{a - x}}\)
\( = \,\frac{{2.303}}{{0.0693\,\,da{y^{ - 1}}}}\,{\log _{10}}\,\frac{1}{{1 - (1/4)}} = 4.1\,days\)