Question

1. an element has three naturally occurring isotopes. information about each isotope is summarized below.

a. find the atomic mass of this element. show all your work.
b. identify the element, using the periodic table.
c. write each isotope in symbolic notation.

Explanation:

Step1: Calculate the contribution of each isotope

For Isotope 1: \(23.985\times\frac{78.70}{100}=23.985\times0.787 = 18.8762\)
For Isotope 2: \(24.946\times\frac{10.13}{100}=24.946\times0.1013 = 2.5270\)
For Isotope 3: \(25.983\times\frac{11.17}{100}=25.983\times0.1117 = 2.9023\)

Step2: Sum up the contributions

\(18.8762 + 2.5270+2.9023=24.3055\)

Answer:

a. The atomic mass of the element is \(24.31\) amu (rounded to two decimal places).
b. Looking at the periodic table, the element with an atomic mass of approximately \(24.31\) amu is magnesium (\(Mg\)).
c.

• Isotope 1: \(\ce{^{24}_{12}Mg}\) (since the mass number is approximately \(24\) and atomic number of \(Mg\) is \(12\))
• Isotope 2: \(\ce{^{25}_{12}Mg}\) (mass number approximately \(25\))
• Isotope 3: \(\ce{^{26}_{12}Mg}\) (mass number approximately \(26\))