Copper has two isotopes. The Cu-63 isotope weighs 62.9296 amu and has 69.17% of the natural abundance. What is the atomic mass (in amu) of the second copper isotope if the average atomic mass of copper is 63.546 amu?

• A. 64.9278 amu
• B. 62.0000 amu
• C. 63.0000 amu
• D. 65.0000 amu

Answer: (A)

Verified step by step guidance

1. Understand that the average atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundances.
2. Let the mass of the second copper isotope be denoted as \( m_2 \) and its natural abundance as \( x \). Since the total abundance must be 100%, the abundance of the second isotope is \( 100\% - 69.17\% = 30.83\% \).
3. Set up the equation for the average atomic mass: \( 63.546 = (62.9296 \times 0.6917) + (m_2 \times 0.3083) \).
4. Rearrange the equation to solve for \( m_2 \): \( m_2 = \frac{63.546 - (62.9296 \times 0.6917)}{0.3083} \).
5. Substitute the known values into the equation and solve for \( m_2 \) to find the atomic mass of the second copper isotope.