(a) Determine the number of carbon `._6^(14)C` atoms present for every gram of carbon `._6^(12)C` in a living organism. Find (b) The decay constatnt and (c ) the activity of this sample.

Explanation

Let's solve the problem step by step.

### Step 1: Determine the number of carbon-14 atoms per gram of carbon-12.

1. **Understanding the ratio**: It is given that for every \(8.3 \times 10^{11}\) atoms of carbon-12, there is 1 atom of carbon-14.

2. **Calculate the number of carbon-12 atoms in 1 gram**:
- The number of atoms in 1 mole of any substance is given by Avogadro's number, \(N_A = 6.022 \times 10^{23}\).
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