Question

The half-life of carbon-14 is 5370 years. The carbon-14 levels in a fossil indicate that 6 half-lives have passed. How old is the fossil?

32,220 years
75,200 years
50,000 years
35,000 years

Answer 1

On half life is 5370 years; 6 half lives have passed. You just multiply,

5370*6 = 32,220 years

Answer 2

Answer: 35,000 years

Explanation: Radioactive process follow first order kinetics.

To calculate the rate constant, we use the formula:

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

`k=(0.693)/(5370years)}`

`k=1.2* 10^(-4) years^(-1)`

Also :
`a=(a_o)/(2^n)`

where,

a = amount of reactant left after n-half lives

`a_o` = Initial amount of the reactant

n = number of half lives = 6

Putting values in above equation, we get:

`2^6=(a_0)/(a)`

`64=(a_0)/(a)`

The rate expression for first order kinetics is given by:

`t=(2.303)/(k)\log(a_0)/(a)`

where,

k = rate constant

t = time taken for decay process

`a_0` = initial amount of the reactant

a = amount left after decay process

Putting values in above equation, we get:

`t=(2.303)/(1.2* 10^(-4))\log{64}`

`t=35000years`