Element E has a relative atomic mass of 12.011 and exists as two naturally occurring isoto… — JAMB UTME

Element $E$ has a relative atomic mass of $12.011$ and exists as two naturally occurring isotopes: $^{12}\text{E}$ with a natural abundance of $98.9\%$ and $^{A}\text{E}$ with a natural abundance of $1.1\%$ . What is the mass number ( $A$ ) of the second isotope?

Answer: 13

Answer

The mass number of the second isotope is 13.

Relative atomic mass is calculated as the weighted average of the mass numbers of all naturally occurring isotopes. Setting up the equation

12.011 = \frac{(98.9 \times 12) + (1.1 \times A)}{100}

yields

1201.1 = 1186.8 + 1.1A

, which simplifies to

1.1A = 14.3

and gives

A = 13

Step-by-Step Solution

State the relationship for relative atomic mass based on isotopic abundance.

\text{RAM} = \frac{(\text{Abundance}_1 \times \text{Mass}_1) + (\text{Abundance}_2 \times \text{Mass}_2)}{100}

Relative atomic mass is the weighted average of the atomic masses of naturally occurring isotopes of an element.

Substitute the given numerical values into the formula.

12.011 = \frac{(98.9 \times 12) + (1.1 \times A)}{100}

Inserting the known abundances (

98.9\%

and

1.1\%

) and mass number (

12

) sets up an algebraic equation for the unknown mass number

A

Solve the algebraic equation for

A

1201.1 = 1186.8 + 1.1A \implies 1.1A = 14.3 \implies A = 13

Subtracting the contribution of the first isotope and dividing by the abundance of the second isotope gives the integer mass number

13

Key Concept

Calculating isotopic mass number from relative atomic mass and fractional abundances

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