Question

The half-life of a substance is the amount of time it takes for half of the amount of substance to decay. The half-life of a pesticide is 2 years. Initially there are 500 grams of pesticide. How much pesticide is left after 10 years? Round to the nearest hundredth.

Answer 1

Answer:

15.625 grams

Step-by-step explanation:

The decay is First order reaction

The half life of the first order reaction is given by

T(1/2)  = ㏑2/K

where K is the reaction constant for the first order reaction

T(1/2) = 2

2 = ln 2 /K

K = ln2/2

The equation of the first order reaction is given by

Kt = ln ($\frac{Ro}{R}$)

where

t = time = 10years

Ro = initial concentration

R = amount left after time t

upon substituting the values

$\frac{ln2}{2}*10 = ln( \frac{500}{R})$

5ln2 = ln (500/R)

ln $2^5$ = ln (500/R)          (a*lnb = ln$b^a$)

$2^5 = 500/R$

R = 500/32  = 15.625grams

Therefore the amount of pesticide left after 10 years is 15.625grams