Question

A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 45 years ago. If the​ half- life of the substance is 20 ​years, what was the density of the substance when it was deposited 45 years​ ago?

Answer 1

Answer:

Given,

D = 7 mg/cm2

t = 45 years

t 1/2 = 20 years

consider,

D = Do e^kt ----->(1)

where as

K = -ln 2/ t1/2

K = -ln 2 / 20

Now substitute K in (1)

7 = Do e^-ln2 *45/20

7 = Do e^ -(9 ln 2)/4

Do = 7 e^(9 ln 2)/4

Do = 7* 4.75683

Do = 33.3 mg/cm^2