To determine the atomic mass of the second isotope of copper (Cu), we can use the information provided about the average atomic mass and the abundance of the first isotope.
Given:
- Average atomic mass of copper (Cu): 63.546 amu
- Isotope Cu-63 atomic mass: 62.9296 amu
- Abundance of Cu-63: 69.15%
We can set up the following equation to solve for the atomic mass of the second isotope (Cu-65):
Average atomic mass = (Atomic mass of Cu-63 * Abundance of Cu-63) + (Atomic mass of Cu-65 * Abundance of Cu-65)
63.546 amu = (62.9296 amu * 69.15%) + (Atomic mass of Cu-65 * Abundance of Cu-65)
Let's solve for the atomic mass of Cu-65:
63.546 amu = (62.9296 amu * 0.6915) + (Atomic mass of Cu-65 * Abundance of Cu-65)
63.546 amu = 43.5391 amu + (Atomic mass of Cu-65 * Abundance of Cu-65)
Atomic mass of Cu-65 * Abundance of Cu-65 = 63.546 amu - 43.5391 amu
Atomic mass of Cu-65 * Abundance of Cu-65 = 20.0069 amu
Now, divide both sides by the abundance of Cu-65:
Atomic mass of Cu-65 = (20.0069 amu) / (Abundance of Cu-65)
To find the atomic mass of Cu-65, we need the value of the abundance of Cu-65. If the abundance of Cu-63 is 69.15%, the abundance of Cu-65 can be calculated by subtracting the abundance of Cu-63 from 100%:
Abundance of Cu-65 = 100% - 69.15%
Abundance of Cu-65 = 30.85%
Finally, substitute the abundance of Cu-65 into the equation:
Atomic mass of Cu-65 = (20.0069 amu) / (0.3085)
Atomic mass of Cu-65 ≈ 64.934 amu
Therefore, the atomic mass of the second isotope, Cu-65, is approximately 64.934 amu.