Answer:
The correct option is;
a. 12.5 g
Explanation:
The given parameters are;
The initial mass of the radioactive substance = 200 g
The half life of the radioactive substance = 50 years
The time duration for the disintegration = 200 years
The formula for half life is given as follows;
[tex]N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}[/tex]
Where:
N(t) = Quantity of the remaining substance
N₀ = Initial radioactive substance quantity = 200 g
t = Time duration = 200 years
[tex]t_{1/2}[/tex] = Half life of the radioactive substance 50 years
Therefore, we have;
[tex]N(t) =200 \times \left (\dfrac{1}{2} \right )^{\dfrac{200}{50} } =200 \times \left (\dfrac{1}{2} \right )^4 = 12.5 \ g[/tex]
Therefore, at the end of 200 years, the quantity left = 12.5 g.
