An element consists of 3 isotopes in nature. Isotope #1, with a mass of X, has a 30% isotopic abundance. Isotope #2, with a mass of Y, has a 60% isotopic abundance. Isotope #3, with a mass of Z, has a 10% isotopic abundance. The atomic weight of this element would be closest to which mass: X, Y, or Z
The Correct Answer and Explanation is:
The correct answer is: Y
Explanation:
An element’s atomic weight is calculated as the weighted average of the masses of its naturally occurring isotopes, based on their relative abundances.
In this case, we are given:
- Isotope #1: Mass = X, Abundance = 30%
- Isotope #2: Mass = Y, Abundance = 60%
- Isotope #3: Mass = Z, Abundance = 10%
To calculate the atomic weight of the element, we use the formula:
Atomic weight = (fraction of X × X) + (fraction of Y × Y) + (fraction of Z × Z)
Let’s substitute the abundances as decimal fractions:
- 30% = 0.30
- 60% = 0.60
- 10% = 0.10
So the equation becomes:
Atomic weight = 0.30 × X + 0.60 × Y + 0.10 × Z
Because isotope #2 (mass Y) has the largest abundance at 60%, it contributes the most to the weighted average. Even if the exact values of X, Y, and Z are not provided, the result of the weighted average will be pulled more heavily toward the mass of isotope Y because its contribution is the greatest.
Here is an example using hypothetical masses:
- X = 10 u
- Y = 20 u
- Z = 30 u
Then the atomic weight would be:
= (0.30 × 10) + (0.60 × 20) + (0.10 × 30)
= 3 + 12 + 3
= 18 u
In this case, the atomic weight (18 u) is closer to Y (20 u) than to X or Z. This example illustrates how the most abundant isotope heavily influences the average.
Therefore, the atomic weight of this element would be closest to mass Y.
