The table below gives the atomic mass and relative abundance values for the three isotopes of element [tex][tex]$M$[/tex][/tex].

\begin{tabular}{|l|l|}
\hline
Relative abundance (\%) & Atomic mass (amu) \\
\hline
78.99 & 23.9850 \\
\hline
10.00 & 24.9858 \\
\hline
11.01 & 25.9826 \\
\hline
\end{tabular}

What is the average atomic mass (in [tex][tex]$amu$[/tex][/tex]) of element [tex][tex]$M$[/tex][/tex]?

A. 2.86
B. 5.36
C. 24.30
D. 24.98



Answer :

To determine the average atomic mass of element [tex]\( M \)[/tex] given the relative abundances and atomic masses of its isotopes, follow these steps:

1. List the given data:
- Relative abundances ([tex]\( \% \)[/tex]) of the isotopes:
- Isotope 1: [tex]\( 78.99\% \)[/tex]
- Isotope 2: [tex]\( 10.00\% \)[/tex]
- Isotope 3: [tex]\( 11.01\% \)[/tex]

- Atomic masses ([tex]\( \text{amu} \)[/tex]) of the isotopes:
- Isotope 1: [tex]\( 23.9850 \text{ amu} \)[/tex]
- Isotope 2: [tex]\( 24.9858 \text{ amu} \)[/tex]
- Isotope 3: [tex]\( 25.9826 \text{ amu} \)[/tex]

2. Convert the relative abundances to fractions:
- Isotope 1: [tex]\( \frac{78.99}{100} = 0.7899 \)[/tex]
- Isotope 2: [tex]\( \frac{10.00}{100} = 0.1000 \)[/tex]
- Isotope 3: [tex]\( \frac{11.01}{100} = 0.1101 \)[/tex]

3. Multiply each atomic mass by its respective fractional abundance:
- Contribution of Isotope 1: [tex]\( 0.7899 \times 23.9850 = 18.9521815 \)[/tex]
- Contribution of Isotope 2: [tex]\( 0.1000 \times 24.9858 = 2.49858 \)[/tex]
- Contribution of Isotope 3: [tex]\( 0.1101 \times 25.9826 = 2.85425426 \)[/tex]

4. Sum these contributions to get the weighted average atomic mass:
[tex]\[ \text{Average atomic mass} = 18.9521815 + 2.49858 + 2.85425426 = 24.30501576 \][/tex]

Therefore, the average atomic mass of element [tex]\( M \)[/tex] is:
[tex]\[ \boxed{24.30 \, \text{amu}} \][/tex]