Element X exists naturally as three isotopes with mass numbers 24, 25, and 26. The relativ… — JAMB UTME

Element $X$ exists naturally as three isotopes with mass numbers $24$ , $25$ , and $26$ . The relative atomic mass of element $X$ is $24.32$ . If the natural abundance of the isotope $^{25}X$ is $10\%$ , what is the percentage abundance of the isotope $^{26}X$ ?

Answer: 11 %

Answer

The percentage abundance of

^{26}X

11\%

By setting the percentage abundance of

^{24}X

x

and

^{26}X

z

, given

^{25}X = 10\%

, we have

x + z = 90\%

. Using the relative atomic mass formula

24x + 25(10) + 26z = 2432

and substituting

x = 90 - z

yields

2410 + 2z = 2432

, solving to

z = 11\%

Step-by-Step Solution

Formulate the abundance relation for the three isotopes.

The sum of abundances is

x + 10 + z = 100\%

, which gives

x = 90 - z

The sum of percentage abundances of all naturally occurring isotopes of an element must equal 100%.

Set up the weighted relative atomic mass equation.

24x + 25(10) + 26z = 2432

Relative atomic mass is the weighted average of isotopic masses based on fractional abundance.

Substitute

x = 90 - z

and solve for

z

24(90 - z) + 250 + 26z = 2432 \implies 2410 + 2z = 2432 \implies z = 11\%

Substituting

x

reduces the equation to a single variable

z

, representing the percentage abundance of

^{26}X

Key Concept

Calculation of Isotopic Abundances from Relative Atomic Mass

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