Atomic Mass and Isotopes?

📌 CONCEPT: The average atomic mass of an element can be calculated using the atomic masses and abundance of its isotopes. This concept is based on the weighted average of the atomic masses of the isotopes present in a sample. The atomic masses of the isotopes are multiplied by their respective abundance percentages to get the weighted average.

📐 RULE / FORMULA: The formula to calculate the average atomic mass is: Average Atomic Mass = (Abundance of isotope 1 * Atomic Mass of isotope 1) + (Abundance of isotope 2 * Atomic Mass of isotope 2) + ... . In this case, it becomes: Average Atomic Mass = (Abundance of ¹²C * Atomic Mass of ¹²C) + (Abundance of ¹³C * Atomic Mass of ¹³C).

💡 WORKED EXAMPLE: Let's consider the given problem. Given that the average atomic mass of carbon is 12.02 u, and it contains 85% of ¹²C and 15% of ¹³C. We can use the formula to calculate the abundance of ¹²C and ¹³C: (0.85 * 12) + (0.15 * 13) = 10.2 + 1.95 = 12.15. But this is not the question, we just need to solve for ¹²C and ¹³C, which is the same as the previous problem, and is simply 0.85 and 0.15 respectively.

⚠️ COMMON MISTAKE: Students often get confused with the calculation of abundance and average atomic mass. They may incorrectly assume that the average atomic mass is equal to the atomic mass of the most abundant isotope, ignoring the contribution of other isotopes.