Questions: Element X has three naturally occurring isotopes. The masses (amu) and % abundances of the isotopes are given in the table below. The average atomic mass of the element is amu. Isotope Abundance Mass 38X 5.07 37.919 39X 15.35 39.017 42X 79.85 42.111

Solution Steps

We need to calculate the average atomic mass of element \( X \) using the given isotopic masses and their respective abundances. The average atomic mass is calculated as the weighted average of the isotopic masses.

The formula for the average atomic mass is: \[ \text{Average Atomic Mass} = \sum (\text{Abundance of Isotope} \times \text{Mass of Isotope}) \] where the abundance is expressed as a fraction (i.e., percentage divided by 100).

Convert the given percent abundances to fractions:

• \( 38\chi \): \( 5.07\% = 0.0507 \)
• \( 39\chi \): \( 15.35\% = 0.1535 \)
• \( 42\chi \): \( 79.85\% = 0.7985 \)

Calculate the contribution of each isotope to the average atomic mass:

• Contribution of \( 38\chi \): \( 0.0507 \times 37.919 = 1.9226 \)
• Contribution of \( 39\chi \): \( 0.1535 \times 39.017 = 5.9861 \)
• Contribution of \( 42\chi \): \( 0.7985 \times 42.111 = 33.6121 \)

Add the contributions from each isotope to find the average atomic mass: \[ 1.9226 + 5.9861 + 33.6121 = 41.5208 \]

Final Answer