The atomic mass of element X is 95.99. It has two isotopes, X-95 and X-96. Which is more abundant?
since the atomic mass is a weighted average of the isotopes, and it is much closer to 96 than 95, then X-96 must be far more abundant.
To determine which isotope is more abundant, we need to compare the relative abundance of each isotope.
The atomic mass of an element is the weighted average of the masses of its isotopes, taking into account their relative abundance. It is calculated using the formula:
Atomic mass = (mass of isotope 1 × relative abundance of isotope 1) + (mass of isotope 2 × relative abundance of isotope 2) + ...
We know that the atomic mass of element X is 95.99. We can set up the following equation based on the given information:
95.99 = (95 × r) + (96 × (1-r))
In this equation, r represents the relative abundance of X-95, and (1-r) represents the relative abundance of X-96. Since there are only two isotopes, the sum of the relative abundances should be equal to 1.
Simplifying the equation, we get:
95.99 = 95r + 96 - 96r
95.99 = 96 - r
r = 96 - 95.99
r ≈ 0.01
Therefore, the relative abundance of X-95 is approximately 0.01, and the relative abundance of X-96 would be (1 - 0.01) = 0.99.
Based on this calculation, we can conclude that X-96 is more abundant than X-95, with a relative abundance of approximately 0.99.