Question

part a
a fictional element has two isotopes and an atomic mass of 87.08 amu. if the first isotope is 86 amu and the second isotope has a mass of 90 amu. which isotope has the greatest natural abundance?
90 amu
86 amu
there are equal amounts
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Explanation:

Step1: Let the abundance of the first isotope ($86$ amu) be $x$, then the abundance of the second isotope ($90$ amu) is $1 - x$.

The formula for atomic mass ($M$) of an element with two isotopes is $M=m_1x + m_2(1 - x)$, where $m_1$ and $m_2$ are the masses of the isotopes.
We know that $M = 87.08$ amu, $m_1=86$ amu, and $m_2 = 90$ amu.
Substitute these values into the formula: $87.08=86x+90(1 - x)$.

Step2: Expand and solve the equation.

Expand $86x+90(1 - x)$: $86x+90 - 90x=87.08$.
Combine like - terms: $- 4x=87.08 - 90=-2.92$.
Solve for $x$: $x=\frac{-2.92}{-4}=0.73$.
The abundance of the $86$ amu isotope is $x = 0.73$ (or $73\%$), and the abundance of the $90$ amu isotope is $1 - x=1 - 0.73 = 0.27$ (or $27\%$).

Answer:

$86$ amu