Question

What is the age of a sample if there are 6 grams of an element that have not decayed out an original 24 grams and has a half-life of 8yrs. a. 8yrs b. 50yrs c. 29yrs d. 16yrs

Answer 1

16 years is the age of a sample.

Step-by-step explanation:

The equation used to calculate half life for first order kinetics:

`t_(1/2)=(0.693)/(k)`

`k=(2.303)/(t)\log([A_o])/([A])`

where,

k = rate constant

`t_(1/2)`= half life of the sample

t = time taken for decay process

`[A_o]` = initial amount of the sample

[A] = amount left after decay process

We are given:

`[A_o]` = 24 grams

[A] = 6 grams

`t_(1/2)= 8 years`

Putting values in above equation, we get:

`k=(0.693)/(8 years)=0.086625 year^(-1)`

Rate law expression for first order kinetics is given by the equation:

`t=(2.303)/(k)\log([A_o])/([A])`

On substituting the values we get value of t:

t = 16.00 years

16 years is the age of a sample.