Question

A wooden artifact from a Chinese temple has a 14C activity of 42.8 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. Part A From the half-life for 14C decay, 5715 yr, determine the age of the artifact.

Answer 1

To determine the age of the artifact, use the ratio of its activity to the standard's activity and the half-life formula for 14C decay. The age of the artifact is approximately 3790 years.

Step-by-step explanation:

To determine the age of the artifact, we can use the half-life of 14C decay, which is 5715 years. The activity of the artifact is 42.8 counts per minute compared to 58.2 counts per minute for a standard of zero age. We can use the ratio of the artifact's activity to the standard's activity to calculate the fraction of 14C remaining in the artifact. From there, we can use the half-life formula to calculate the age of the artifact.

Using the formula A / Ao = (1/2)^(t / half-life), where A is the current activity, Ao is the initial activity, t is the time passed, and half-life is 5715 years, we can solve for t to find the age of the artifact. Rearranging the formula gives us t = -half-life * log(A / Ao) / log(1/2).

Plugging in the values, we have A = 42.8, Ao = 58.2, and half-life = 5715. Solving the equation, we find that the age of the artifact is approximately 3790 years.

Answer 2

Answer : The age of the artifact is,
`2.54* 10^3\text{ years}`

Explanation :

Half-life = 5715 years

First we have to calculate the rate constant, we use the formula :

`k=\frac{0.693}{5715\text{ years}}`

`k=1.21* 10^(-4)\text{ years}^(-1)`

Now we have to calculate the time taken to decay.

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = time taken by sample = ?

a = initial activity of the reactant = 58.2 counts per minute

a - x = activity left after decay process = 42.8 counts per minute

Now put all the given values in above equation, we get

`t=(2.303)/(1.21* 10^(-4))\log(58.2)/(42.8)`

`t=2540.5\text{ years}=2.54* 10^3\text{ years}`

Therefore, the age of the artifact is,
`2.54* 10^3\text{ years}`