A naturally occurring element X consists of two stable isotopes, ^{63}X and ^{65}X. If the… — JAMB UTME

A naturally occurring element $X$ consists of two stable isotopes, $^{63}X$ and $^{65}X$ . If the relative atomic mass of element $X$ is $63.6$ , what is the percentage abundance of the heavier isotope $^{65}X$ ?

$30\%$ Answer
B
$70\%$
C
$60\%$
D
$50\%$

Answer

The percentage abundance of the heavier isotope

^{65}X

30\%

The relative atomic mass of an element with isotopes is calculated using the weighted average formula:

\text{RAM} = \sum (\text{mass} \times \text{fractional abundance})

. Setting

p

as the fraction of

^{65}X

gives

63.6 = 63(1 - p) + 65p = 63 + 2p

. Solving yields

2p = 0.6

, so

p = 0.30

, which corresponds to

30\%

Step-by-Step Solution

Set up the relative atomic mass weighted average equation

63.6 = \frac{(m_1 \times x_1) + (m_2 \times x_2)}{100}

Relative atomic mass is the weighted average of the atomic masses of naturally occurring isotopes based on their fractional abundances.

Express isotopic abundances in terms of a single variable

p

Let

p

be the fraction of

^{65}X

, so the fraction of

^{63}X

1 - p

The sum of the fractional abundances of all isotopes of an element must equal 1 (or

100\%

Substitute known values and solve for

p

63.6 = 63(1 - p) + 65p \implies 63.6 = 63 + 2p \implies 2p = 0.6 \implies p = 0.30

Algebraic expansion isolates the variable corresponding to the heavier isotope abundance.

Convert the fractional abundance to percentage

0.30 \times 100\% = 30\%

Multiplying the decimal fraction by 100 yields the percentage abundance.

Key Concept

Calculation of Relative Atomic Mass from Isotopic Abundance

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic