Question

A sample of radium has a weight of 1.5 mg and decays

Answer 1

Answer: $(b)$

Step-by-step explanation:

Given

Initial mass of radium is $A_o=1.5\ mg$

It decays by half every 6 years i.e. $T_{\frac{1}{2}}=6$

For radioactive decay, sample at any time is given by

$\Rightarrow A=A_o2^{-\dfrac{t}{T_{\frac{1}{2}}}}$

Insert the values

$\Rightarrow A=1.5\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot \left(\dfrac{1}{2}\right)^{\dfrac{-t}{6}}\\\\\Rightarrow A=1.5\cdot (0.5)^{\dfrac{t}{6}}$

Thus, option  (b) is correct.