Question

How would you calculate the percent relative abundance of $Cu - 63$ with the mass $62.9296{\text{ }}g$ and $Cu - 65$ with the mass $64.9278{\text{ }}g$ , when the average mass of Cu is $63.546$ ?

Answer 1

The relative abundance definition in science is the percentage of a specific isotope that happens in nature. The nuclear mass listed for a component on the periodic table is an average mass of all known isotopes of that component.

Complete step by step answer:
As you most likely are aware, the average nuclear mass of a component is determined by taking the weighted average of the nuclear masses of its normally occurring isotopes.
Step 1: Find the Average Atomic Mass
Basically, a component's normally occurring isotopes will contribute to the average nuclear mass of the component relative to their abundance.
$avg.{\text{ }}atomic{\text{ }}mass$ =$\sum \left( {{\text{isotope}} \times {\text{abundance}}} \right)$
Step 2: Set Up the Relative Abundance Problem
With regards to the genuine count, it's simpler to use decimal abundances, which are basically percent abundances divided by $100$ .
Thus, you realize that copper has two naturally occurring isotopes, $copper - 63$ and $copper - 65$ . This implies that their respective decimal abundance should amount to give$1$ .
In the event that you take x to be the decimal bounty of $copper - 63$ , you can say that the decimal abundance of $copper - 65$ will be equivalent to $1 - x$ .
So we can say that:
$x \cdot 62.9296u + (1 - x) \cdot 64.9278u = 63.546u$
Step 3: Solve for x to Get the Relative Abundance of the Unknown Isotope.
To finding the value of x we get
$62.9296 \cdot x - 64.9278 \cdot x = 63.546 - 64.9278$ $1.9982 \cdot x = 1.3818$
$x =$ $\dfrac{{1.38181}}{{0.9982}}$
$x = {\text{ }}0.69152$
Step 4: Find percent abundance
This implies that the percent abundances of the two isotopes will be
$69.152\%$---->$^{63}Cu$
$30.848\%$------.$^{65}Cu$

Note:
If a mass spectrum of the component was given, the relative rate isotope abundances are generally introduced as a vertical bar graph. The all-out may look as though it exceeds $100\% ,$ however, that is because the mass spectrum works with relative rate isotope abundances.