Answer:
27.5 minutes
Step-by-step explanation:
Using,
R/R' = 2ᵃ/ᵇ------------------ Equation 1
From the equation,
R = mass of Element X before radioactive decay, R' = mass of element X after radioactive decay, a = Time taken, b = half life.
Given: R = 870 grams, R' = 154 grams, b = 11 minutes.
Substitute these values into equation 1
870/154 = 2ᵃ/¹¹
(870/154)¹¹ = 2ᵃ
Solve for a
2ᵃ = (5.649)¹¹
2ᵃ = 187061.26
Taking the logarithm of both side,
Log2ᵃ = Log(187061.26)
⇒ a = log(187061.26)/log2
a = 8.272/0.301
a = 27.5 minutes
