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

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

[tex]\[
\begin{array}{|l|l|}
\hline
\text{Relative abundance (\%)} & \text{Atomic mass (amu)} \\
\hline
78.99 & 23.9850 \\
\hline
10.00 & 24.9858 \\
\hline
11.01 & 25.9826 \\
\hline
\end{array}
\][/tex]

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

Sagot :

GinnyAnswer
To find the average atomic mass of element [tex]\(M\)[/tex], we need to consider the relative abundances and the atomic masses of its isotopes. The calculation involves the following steps:

1. Extract Data:
- Relative abundances: 78.99%, 10.00%, 11.01%
- Atomic masses: 23.9850 amu, 24.9858 amu, 25.9826 amu

2. Calculate the weighted atomic masses:
- For the first isotope: [tex]\( 78.99 \times 23.9850 = 1894.57515 \)[/tex]
- For the second isotope: [tex]\( 10.00 \times 24.9858 = 249.858 \)[/tex]
- For the third isotope: [tex]\( 11.01 \times 25.9826 = 286.068426 \)[/tex]

3. Calculate the total relative abundance:
- [tex]\( 78.99 + 10.00 + 11.01 = 100.0 \)[/tex]

4. Calculate the average atomic mass:
- Sum of weighted atomic masses:
[tex]\( 1894.57515 + 249.858 + 286.068426 = 2430.501576 \)[/tex]
- Divide the sum by the total relative abundance:
[tex]\( \frac{2430.501576}{100.0} = 24.30501576 \)[/tex]

So, the average atomic mass of element [tex]\(M\)[/tex] is approximately [tex]\(24.30\)[/tex] amu. Therefore, the correct answer is:

24.30
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