Element Y exists naturally as two isotopes, ^{63}Y and ^{65}Y. If the relative atomic mass… — JAMB UTME

Element $Y$ exists naturally as two isotopes, $^{63}Y$ and $^{65}Y$ . If the relative atomic mass of element $Y$ is $63.5$ , what is the percentage abundance of the lighter isotope, $^{63}Y$ ?

$75\%$ Answer
B
$25\%$
C
$50\%$
D
$35\%$

Answer

The percentage abundance of the lighter isotope

^{63}Y

75\%

The percentage abundance is calculated using the weighted average formula:

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

. Substituting the given values yields

63.5 = \frac{63x + 65(100-x)}{100}

, which simplifies to

-2x = -150

, giving

x = 75\%

for

^{63}Y

Step-by-Step Solution

Define variables for isotopic abundances.

Let the abundance of

^{63}Y

x\%

. The abundance of

^{65}Y

is therefore

(100 - x)\%

The sum of all relative isotopic abundances for a natural element equals

100\%

Set up the weighted average formula for relative atomic mass.

\text{Relative Atomic Mass} = \frac{(63 \times x) + 65 \times (100 - x)}{100} = 63.5

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

Solve the equation for

x

63x + 6500 - 65x = 6350 \implies -2x = -150 \implies x = 75

Simplifying algebraic terms gives the percentage abundance of the lighter isotope.

Key Concept

Isotopic Abundance and Relative Atomic Mass Calculation

Estimated Time:1m 30s

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