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The table below gives the atomic mass and relative abundance values for the three isotopes of element M.

| Relative Abundance (%) | Atomic Mass (amu) |
|-----------------------|-------------------|
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |

What is the average atomic mass (in amu) of element M?

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



Answer :

GinnyAnswer
To find the average atomic mass of element [tex]\( M \)[/tex], we need to consider both the atomic masses of its isotopes and their relative abundances. Here's a step-by-step method to solve the problem:

1. Convert the relative abundances from percentages to fractions:
- For the isotope with a relative abundance of 78.99%: [tex]\( \frac{78.99}{100} = 0.7899 \)[/tex]
- For the isotope with a relative abundance of 10.00%: [tex]\( \frac{10.00}{100} = 0.1000 \)[/tex]
- For the isotope with a relative abundance of 11.01%: [tex]\( \frac{11.01}{100} = 0.1101 \)[/tex]

2. Multiply each atomic mass by its corresponding fractional abundance:
- [tex]\( 23.9850 \, \text{amu} \times 0.7899 = 18.952015 \)[/tex]
- [tex]\( 24.9858 \, \text{amu} \times 0.1000 = 2.49858 \)[/tex]
- [tex]\( 25.9826 \, \text{amu} \times 0.1101 = 2.85442076 \)[/tex]

3. Sum these values to get the average atomic mass:
[tex]\[ 18.952015 + 2.49858 + 2.85442076 = 24.30501576 \, \text{amu} \][/tex]

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

So, the correct answer is:
- [tex]\( 24.30 \)[/tex]

The average atomic mass of element [tex]\( M \)[/tex] is [tex]\( 24.30 \, \text{amu} \)[/tex].

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