Weighted Average of Isotopes Calculator

Weighted Average Formula:

\[ \text{Weighted Average} = \sum (\text{Isotope Mass} \times \text{Fractional Abundance}) \]

Weighted Average:

1. What is Isotope Weighted Average?

The weighted average of isotopes calculates the average atomic mass of an element based on the masses of its naturally occurring isotopes and their relative abundances. This is how atomic weights on the periodic table are determined.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

\[ \text{Weighted Average} = \sum (\text{Isotope Mass} \times \text{Fractional Abundance}) \]

Where:

Isotope Mass — Mass of each isotope in atomic mass units (amu)
Fractional Abundance — Natural abundance of each isotope (as a decimal between 0 and 1)
The sum (Σ) means to add up the products for all isotopes

3. Importance of Weighted Average

Details: The weighted average atomic mass is crucial for chemical calculations and appears on the periodic table. It differs from a simple average because it accounts for how common each isotope is in nature.

4. Using the Calculator

Tips: Enter each isotope's mass in amu and its fractional abundance (e.g., 0.25 for 25%). Click "Add Isotope" for additional isotopes. All abundances should sum to 1 (100%).

5. Frequently Asked Questions (FAQ)

Q1: Why don't we use simple average?
A: Simple average would give equal weight to all isotopes, regardless of how common they are in nature, leading to incorrect atomic mass values.

Q2: What if abundances don't sum to 1?
A: The calculator will still work, but results won't match real-world atomic masses. Natural abundances always sum to 1 (100%).

Q3: How many isotopes can I enter?
A: You can add as many isotopes as needed. Most elements have 2-10 naturally occurring isotopes.

Q4: Where can I find isotope masses and abundances?
A: The IUPAC publishes comprehensive tables of isotopic compositions and atomic weights.

Q5: Why are some atomic masses on periodic tables in brackets?
A: Brackets indicate the standard atomic weight is not a single value but a range, due to natural variation in isotopic composition.