Theatomic mass of copper is 63.55.There are only two isotopes of copper , Cu-63 with a mass of 62.93 amu and Cu-65 w/ a mass of 64.93 amu. What is the percent of each of these two isotopes?

Total is 100%, so assuming x is the fraction of Cu-63, (1-x) is the fraction of Cu-65.

Atomic weight is the (weighted) average of all isotopes.

Therefore you have:

x*62.93 + (1-x)*64.93 = 63.55
x = 0.69.

So you have 69% Cu-63 and 31% Cu-65.

To determine the percentage of each isotope of copper, we need to consider their relative abundances and use the formula:

Percentage = (Relative abundance / Total abundance) x 100

1. First, we need to find the relative abundance of each isotope. We can assume that the sum of the relative abundances is 100%.

Let's call the relative abundance of Cu-63 as "x" and the relative abundance of Cu-65 as "y".

2. Next, we need to calculate the total abundance by using the atomic mass of copper.

Total abundance = (Relative abundance of Cu-63 × Mass of Cu-63) + (Relative abundance of Cu-65 × Mass of Cu-65)

Total abundance = (x × 62.93) + (y × 64.93)

3. We know that the atomic mass of copper is 63.55 amu, which is the weighted average of the two isotopes.

Atomic mass = (Relative abundance of Cu-63 × Mass of Cu-63) + (Relative abundance of Cu-65 × Mass of Cu-65)

63.55 = (x × 62.93) + (y × 64.93)

This equation represents the relationship between the relative abundances and atomic mass.

4. Now, we can solve the system of equations formed by the total abundance and atomic mass equations to find the values of "x" and "y".

63.55 = (x × 62.93) + (y × 64.93) (Equation 1)
Total abundance = (x × 62.93) + (y × 64.93) (Equation 2)

By solving these equations simultaneously, we can determine the values of "x" and "y".

5. Once we have the values of "x" and "y", we can calculate the percentage of each isotope using the formula mentioned above.

Percentage of Cu-63 = (x / (x + y)) × 100
Percentage of Cu-65 = (y / (x + y)) × 100

Substitute the values of "x" and "y" to calculate the percentage of each isotope.

Note: The specific values of "x" and "y" will depend on the relative abundances of the isotopes of copper, which can vary in different samples.