To determine the approximate atomic mass of element X, we need to calculate the weighted average of the atomic masses of its isotopes, considering their relative abundances.
The atomic mass of an isotope is the sum of the number of protons and neutrons in its nucleus. Let's denote the atomic mass of ²⁵X as A₁ and the atomic mass of ²⁷X as A₂.
Given that the abundance of ²⁵X is 80.5% and the abundance of ²⁷X is 19.5%, we can calculate the weighted average as follows:
Atomic mass of X = (A₁ * abundance of ²⁵X) + (A₂ * abundance of ²⁷X)
Plugging in the values:
Atomic mass of X = (A₁ * 0.805) + (A₂ * 0.195)
Since we don't have the exact values for A₁ and A₂, we can use placeholders. Let's use X₁ for A₁ and X₂ for A₂:
Atomic mass of X = (X₁ * 0.805) + (X₂ * 0.195)
Now we need to solve for X₁ and X₂. However, we can simplify the problem by using the fact that the atomic mass is a whole number. We can assume that X₁ and X₂ are integers.
Let's start by trying some reasonable values for X₁ and X₂. We can start with X₁ = 25 (corresponding to ²⁵X) and X₂ = 27 (corresponding to ²⁷X).
Atomic mass of X = (25 * 0.805) + (27 * 0.195) Atomic mass of X ≈ 20.125 + 5.265 Atomic mass of X ≈ 25.39
Since the atomic mass should be a whole number, the assumed values for X₁ = 25 and X₂ = 27 are not correct. We can try different combinations until we find a whole number.
After trying a few different combinations, we find that X₁ = 26 and X₂ = 28 give us a whole number atomic mass:
Atomic mass of X = (26 * 0.805) + (28 * 0.195) Atomic mass of X ≈ 20.93 + 5.46 Atomic mass of X ≈ 26.39
Therefore, the approximate atomic mass of element X is approximately 26.39.