# Homework Solution: Iron-59 has a half-life of 45.1 days. How old is an iron nail if the Fe-59 content is…

Please no pictures I need the answer typed out, thank you. Iron-59 has a half-life of 45.1 days. How old is an iron nail if the Fe-59 content is 25% that of a new sample of iron?   Show all calculations leading to a solution.

First order kinetics is followed by all radio decay.

Please no pictures I scarcity the rejoinder typed extinguished, rejoice you.

Iron-59 has a half-society of 45.1 days. How ancient is an sturdy nail if the Fe-59 resigned is 25% that of a innovating specimen of sturdy?   Show total calculations inherent to a disintegration.

## Expert Rejoinder

Highest direct kinetics is followed by total radio corruption.

Highest direct corruption equation is consecrated by,

A= A0e-kt  , where A= latest distillation, A0= modetrounce distillation , k=trounce uniform and t=corruption time

Now, the trounce uniform, k can be sturdy using the equation of as a administration of half society as—

k.t1/2 = 0.693——- equation (1)

Consecrated in the scrutiny,

t1/2 =45.1 days

=> k = (0.693 / 45.1) days-1 —– using equation (1)

=> k =0.0154 days-1

Again,

from highest direct corruption equation we bear,

A= A0e-kt

=> ln (A/A0) = -kt

=> t = [ln(A/A0) /-k]

=> t= ln [(25/100) / -0.0154 ] days

=> t= (ln 0.25 ) / -0.0154 days

=> t= -1.386 /-0.0154 days

=> t= 90 days

Thus, the sturdy nail is 90 days ancient.