Question

An element has two isotopes having atomic masses 10 and 15 u, respectively. If the percent abundance of lighter isotopes is 80%, then the average atomic mass of the element is:

• A. $ 9 \, \text{u} $
• B. $ 11 \, \text{u} $
• C. $ 12 \, \text{u} $
• D. $ 14 \, \text{u} $

Hint:

Key points to remember:

• Average mass is weighted by natural abundance
• Percent abundances must sum to 100\%
• No need for complex formulas
  - simple weighted average suffices
• Units remain atomic mass units (u) throughout

Answer 1

The Correct Option is B

Step 1: Identify given data
- Isotope 1 mass = $10 \, \text{u}$ (80% abundance)
- Isotope 2 mass = $15 \, \text{u}$ (20% abundance)
Step 2: Calculate average atomic mass
\[ \text{Average mass} = \left(\frac{80}{100} \times 10\right) + \left(\frac{20}{100} \times 15\right) \] \[ = (0.8 \times 10) + (0.2 \times 15) \] \[ = 8 + 3 = 11 \, \text{u} \]
Step 3: Verify calculation
- Contribution from lighter isotope: $10 \times 0.8 = 8 \, \text{u}$
- Contribution from heavier isotope: $15 \times 0.2 = 3 \, \text{u}$
- Total average mass = $8 + 3 = 11 \, \text{u}$
Step 4: Match with options
The calculated average mass of $11 \, \text{u}$ corresponds to option (b).