Question

The previous part could be done without using the decay equation, because the ratio of original 14C to present 14C was an integer power of 1/2. Most problems are not so simple. To solve more general carbon-dating problems, you must first find the value of the decay constant for 14C, so that you can easily use the decay equation. Using the given half-life, 5730 years, find the value of the decay constant for 14C.

Answer 1

0.000121 year⁻¹

Step-by-step explanation:

The half life is defined as the time at which the reactant's concentration reduced to half.

The formula for the half life for a first order kinetic reaction is:

`t_(1/2)=\frac {ln\ 2}{k}`

Where,

`t_(1/2)` is the half life

k is the rate constant.

Thus, Given that:

Half life = 5730 years

`t_(1/2)=\frac {ln\ 2}{k}`

Where, k is rate constant

So,

`k=\frac {ln\ 2}{t_(1/2)}`

`k=\frac {ln\ 2}{5730}\ years^(-1)`

The rate constant or decay constant, k = 0.000121 year⁻¹