Question

If you have a 200g sample of a radioactive isotope that has a half life of 50 years, hc

Answer 1

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;

$N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}$

Where:

N(t) = Quantity of the remaining substance

N₀ = Initial radioactive substance quantity  = 200 g

t = Time duration  = 200 years

 

$t_{1/2}$ = Half life of the radioactive substance  50 years

Therefore, we have;

$N(t) =200 \times \left (\dfrac{1}{2} \right )^{\dfrac{200}{50} } =200 \times \left (\dfrac{1}{2} \right )^4 = 12.5 \ g$

Therefore, at the end of 200 years, the quantity left = 12.5 g.