Radioactive decay is a first`-` order process. Radioactive carbon in wood sample decays with a half`-` life of 5770 years. What is the rate constant `(` in years `)` for the decay ? What fraction would remains after 11540 years ?

Explanation

To solve the problem step by step, we will first calculate the rate constant for the radioactive decay of carbon and then determine the fraction of carbon remaining after a specified time.

### Step 1: Calculate the Rate Constant (k)

The relationship between the half-life (t₁/₂) and the rate constant (k) for a first-order reaction is given by the formula:

\[
k = \frac{0.693}{t_{1/2}}
...