Answer: [tex](b)[/tex]
Step-by-step explanation:
Given
Initial mass of radium is [tex]A_o=1.5\ mg[/tex]
It decays by half every 6 years i.e. [tex]T_{\frac{1}{2}}=6[/tex]
For radioactive decay, sample at any time is given by
[tex]\Rightarrow A=A_o2^{-\dfrac{t}{T_{\frac{1}{2}}}}[/tex]
Insert the values
[tex]\Rightarrow A=1.5\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot \left(\dfrac{1}{2}\right)^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot (0.5)^{\dfrac{t}{6}}[/tex]
Thus, option (b) is correct.
