Answer :
To calculate the relative atomic mass of potassium, we need to consider the isotopes of potassium and their relative abundances. The relative atomic mass is essentially a weighted average of the masses of the isotopes.
Potassium has two major isotopes:
- [tex]^{39}\text{K}[/tex] with a relative abundance of 93%
- [tex]^{41}\text{K}[/tex] with a relative abundance of 7%
The atomic masses of these isotopes are approximately 39 and 41, respectively.
To calculate the relative atomic mass, we will use the formula:
[tex]\text{Relative Atomic Mass} = (\text{Abundance of } ^{39}\text{K} \times \text{Mass of } ^{39}\text{K}) + (\text{Abundance of } ^{41}\text{K} \times \text{Mass of } ^{41}\text{K})[/tex]
Step-by-step calculation:
Convert the percentage abundances into fractions:
- [tex]^{39}\text{K}[/tex] = 93% = 0.93
- [tex]^{41}\text{K}[/tex] = 7% = 0.07
Calculate the contributions from each isotope:
- Contribution from [tex]^{39}\text{K}[/tex]: [tex]0.93 \times 39 = 36.27[/tex]
- Contribution from [tex]^{41}\text{K}[/tex]: [tex]0.07 \times 41 = 2.87[/tex]
Sum these contributions to find the relative atomic mass:
- [tex]36.27 + 2.87 = 39.14[/tex]
However, the multiple-choice options provided do not include exact decimals, so we'll select the closest option, which rounds off to "39.1".
Therefore, the relative atomic mass of potassium is approximately 39.1.
The correct answer is B) 39.1.
