To calculate the relative atomic mass of an element with two isotopes of relative isotopic masses x and x+4, assuming equal abundances, we need to consider the weighted average of the isotopic masses.
The relative atomic mass (Aᵣ) is calculated as follows:
Aᵣ = (abundance₁ × mass₁ + abundance₂ × mass₂) / (abundance₁ + abundance₂)
Given that the abundances of both isotopes are the same, we can assign them equal values of 1/2.
Plugging in the values:
Aᵣ = [(1/2) × x + (1/2) × (x+4)] / [(1/2) + (1/2)]
Simplifying:
Aᵣ = (x + (x+4)) / 2
Aᵣ = (2x + 4) / 2
Aᵣ = (2(x + 2)) / 2
Aᵣ = x + 2
Therefore, the relative atomic mass of the element is given by x + 2.