To calculate the average atomic mass of element [tex]\(M\)[/tex], we can use the weighted average formula based on the given relative abundances and atomic masses of the isotopes.
Here are the values from the table:
1. Relative abundance = 78.99%, Atomic mass = 23.9850 amu
2. Relative abundance = 10.00%, Atomic mass = 24.9858 amu
3. Relative abundance = 11.01%, Atomic mass = 25.9826 amu
Let's convert these percentages to fractional abundances by dividing by 100:
1. [tex]\( \text{Abundance}_1 = \frac{78.99}{100} = 0.7899 \)[/tex]
2. [tex]\( \text{Abundance}_2 = \frac{10.00}{100} = 0.1000 \)[/tex]
3. [tex]\( \text{Abundance}_3 = \frac{11.01}{100} = 0.1101 \)[/tex]
Next, we apply the formula for the weighted average:
[tex]\[ \text{Average atomic mass} = (\text{Abundance}_1 \times \text{Mass}_1) + (\text{Abundance}_2 \times \text{Mass}_2) + (\text{Abundance}_3 \times \text{Mass}_3) \][/tex]
Plugging in the values:
[tex]\[ \text{Average atomic mass} = (0.7899 \times 23.9850) + (0.1000 \times 24.9858) + (0.1101 \times 25.9826) \][/tex]
Performing the multiplications:
1. [tex]\( 0.7899 \times 23.9850 = 18.9584115 \)[/tex]
2. [tex]\( 0.1000 \times 24.9858 = 2.49858 \)[/tex]
3. [tex]\( 0.1101 \times 25.9826 = 2.84802426 \)[/tex]
Adding these results together:
[tex]\[ 18.9584115 + 2.49858 + 2.84802426 = 24.30501576 \][/tex]
Therefore, the average atomic mass of element [tex]\(M\)[/tex] is [tex]\( \boxed{24.30} \)[/tex] amu.
