The time taken for the radioactive element to decay to 1 gram is 25 days.
The half life of a radioactive element is defined as the time taken to decay to its original mass.
N(t) = No(¹/₂)^t/h
where;
when the remaining mass = 1 gram, the time taken is calculated as follows;
1 = 4.2(0.5)^t/12
1/4.2 = (0.5)^t/12
log(1/4.2) = log(0.5)^t/12)
-0.623 = t/12(-0.3)
-0.623/-0.3 = t/12
2.077 = t/12
2.077 x 12 days = t
25 days = t
Thus, the time taken for the radioactive element to decay to 1 gram is 25 days.
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