Element Q occurs naturally as two isotopes, ^{35}Q and ^{37}Q. If the relative atomic mass… — JAMB UTME

Element $Q$ occurs naturally as two isotopes, $^{35}Q$ and $^{37}Q$ . If the relative atomic mass of element $Q$ is $35.5$ , what is the percentage abundance of the heavier isotope $^{37}Q$ ?

25%Answer
B
75%
C
50%
D
35.5%

Answer

The percentage abundance of

^{37}Q

is 25%.

The relative atomic mass (

35.5

) lies between

35

and

37

, closer to

35

. Setting up the weighted average equation

35.5 = \frac{35(100 - x) + 37x}{100}

yields

x = 25\%

for

^{37}Q

, while

^{35}Q

accounts for the remaining

75\%

Step-by-Step Solution

Set up the relative atomic mass equation using percentage abundances.

Let the percentage abundance of

^{37}Q

x\%

. Therefore, the abundance of

^{35}Q

(100 - x)\%

The sum of natural abundances for all isotopes of an element must equal 100%.

Substitute the isotopic mass numbers and relative atomic mass into the weighted average formula.

35.5 = \frac{35(100 - x) + 37x}{100}

Relative atomic mass is calculated as the weighted average of the mass numbers of naturally occurring isotopes.

Solve the linear equation for

x

3550 = 3500 - 35x + 37x \implies 50 = 2x \implies x = 25

Multiplying by 100 and rearranging terms isolates

x = 25

Key Concept

Calculation of isotopic abundances from relative atomic mass

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