There are two naturally occurring isotopes of copper. 63Cu has a mass of 62.9296 amu. 65Cu has a mass of 64.9278 amu. Determine the abundance of each isotope.
You need the average atomic mass, looking at the periodic table, I see 63.546 amu.
average=Isotope1*percent1 + Isotope2*percent2
if you assume only two isotopes, then Isotope2 is 1-percent1
63.546=64.9278(percent65Cu)+62.9296(1-percent65Cu)
solve for the decimal percent of 65Cu.
To determine the abundance of each isotope, we can use the mass and the average atomic weight of copper.
Let's assume there are two isotopes of copper, 63Cu and 65Cu, with corresponding masses of 62.9296 amu and 64.9278 amu, respectively.
Let x represent the abundance of 63Cu (in decimal form), then the abundance of 65Cu would be (1 - x) since the sum of the abundances must be 1.
We can set up the equation as:
62.9296 amu * x + 64.9278 amu * (1 - x) = average atomic weight of copper
The average atomic weight of copper can be found in the periodic table, which is approximately 63.55 amu.
Plugging in the values, we get:
62.9296x + 64.9278(1 - x) = 63.55
Simplifying the equation:
62.9296x + 64.9278 - 64.9278x = 63.55
-2.9982x + 64.9278 = 63.55
-2.9982x = 63.55 - 64.9278
-2.9982x = -1.3778
Dividing by -2.9982:
x ≈ -1.3778 / -2.9982
x ≈ 0.4598
Therefore, the abundance of 63Cu is approximately 0.4598, and the abundance of 65Cu is approximately (1 - 0.4598) = 0.5402.
To express the abundances as percentages, we can multiply by 100:
Abundance of 63Cu ≈ 0.4598 * 100 ≈ 45.98%
Abundance of 65Cu ≈ 0.5402 * 100 ≈ 54.02%
So, the abundance of 63Cu is approximately 45.98%, and the abundance of 65Cu is approximately 54.02%.
To determine the abundance of each isotope, we need to know the concept of weighted average atomic mass or average atomic mass.
The average atomic mass is calculated by considering the abundance and mass of each isotope. The abundance of an isotope is the percentage or fraction of that particular isotope present in a sample.
Let's assume the abundance of 63Cu is x (in decimal form) and the abundance of 65Cu is y (in decimal form).
The average atomic mass can be calculated using the following formula:
Average Atomic Mass = (abundance of 1st isotope × mass of 1st isotope) + (abundance of 2nd isotope × mass of 2nd isotope)
63.546 amu (average atomic mass) = (x × 62.9296 amu) + (y × 64.9278 amu)
Now, we have one equation with two variables. However, we can use additional information to solve for the abundance of each isotope.
Since there are only two naturally occurring isotopes of copper, the sum of their abundances will be equal to 100%. Therefore, we can write a second equation:
x + y = 1
Now we have a system of equations:
x × 62.9296 amu + y × 64.9278 amu = 63.546 amu
x + y = 1
Solving this system of equations will give us the values of x and y, which represent the abundances of each isotope.
Using any algebraic method (substitution, elimination, or matrices), we can solve the system of equations and find the values of x and y.
Once we have the values of x and y, remember to convert them back to percentages (multiply by 100) to get the abundance of each isotope expressed as a percentage.
That's how we can determine the abundance of each isotope using the given information.