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The table below gives the atomic mass and relative abundance values for the three isotopes of element [tex]M[/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 amu) of element [tex]M[/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 first need to consider the atomic masses and relative abundances of its isotopes. The isotopes' data is provided in the table:

| Relative abundance (%) | Atomic mass (amu) |
|------------------------|-------------------|
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |

Here is the step-by-step process:

1. Convert the relative abundances from percentages to fractions:

[tex]\[ \text{Fractional abundance of isotope 1} = \frac{78.99}{100} = 0.7899 \][/tex]

[tex]\[ \text{Fractional abundance of isotope 2} = \frac{10.00}{100} = 0.10 \][/tex]

[tex]\[ \text{Fractional abundance of isotope 3} = \frac{11.01}{100} = 0.1101 \][/tex]

2. Use the formula for average atomic mass:

[tex]\[ \text{Average atomic mass} = (\text{fractional abundance of isotope 1} \times \text{atomic mass of isotope 1}) + (\text{fractional abundance of isotope 2} \times \text{atomic mass of isotope 2}) + (\text{fractional abundance of isotope 3} \times \text{atomic mass of isotope 3}) \][/tex]

3. Substitute the given values into the formula:

[tex]\[ \text{Average atomic mass} = (0.7899 \times 23.9850) + (0.10 \times 24.9858) + (0.1101 \times 25.9826) \][/tex]

4. Compute each term:

[tex]\[ 0.7899 \times 23.9850 = 18.945915 \][/tex]

[tex]\[ 0.10 \times 24.9858 = 2.49858 \][/tex]

[tex]\[ 0.1101 \times 25.9826 = 2.86052026 \][/tex]

5. Sum these values to get the average atomic mass:

[tex]\[ \text{Average atomic mass} = 18.945915 + 2.49858 + 2.86052026 = 24.30501576 \][/tex]

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

Hence, the correct answer is:

[tex]\[ \boxed{24.30} \][/tex]
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