The mass of C-12 and C-14 isotopes are found as 98% and 2% respectively. The number of atoms of C-14 in 12 g of sample are

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1.5 mole atoms

$3.06 \times 10^{22} atoms$

$1.03 \times 10^{22} atoms$

$3.08 \times 10^{22} atoms$

answer is B.

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Detailed Solution

To determine the number of carbon-14 (C-14) atoms in a 12 g carbon sample with isotopic abundances of 98% carbon-12 (C-12) and 2% C-14, follow these steps:

Calculate the mass of C-14 in the sample:
- Since C-14 constitutes 2% of the total carbon mass:
  - Mass of C-14 = 2% of 12 g = 0.02 × 12 g = 0.24 g
Determine the number of moles of C-14:
- The molar mass of C-14 is approximately 14 g/mol.
- Number of moles of C-14 = Mass of C-14 / Molar mass of C-14
  - = 0.24 g / 14 g/mol
  - ≈ 0.01714 mol
Calculate the number of C-14 atoms:
- Using Avogadro's number (6.022 × 10²³ atoms/mol):
  - Number of C-14 atoms = Number of moles × Avogadro's number
  - = 0.01714 mol × 6.022 × 10²³ atoms/mol
  - ≈ 1.032 × 10²² atoms