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If an element X has two isotopes X-30 (abundance 20%) and X-32 (abundance 80%), what is the average atomic mass?
31.2 u
31.6 u
30.8 u
31.0 u
31.6 u
The average atomic mass is calculated as the weighted average of the masses of all naturally occurring isotopes of an element. Since isotopes exist in different proportions, their atomic mass is not a simple arithmetic mean, but a sum of each isotope's mass multiplied by its fractional abundance.
The average atomic mass is calculated as the weighted average of the masses of all naturally occurring isotopes of an element. Since isotopes exist in different proportions, their atomic mass is not a simple arithmetic mean, but a sum of each isotope's mass multiplied by its fractional abundance.
Think of it like a class average for a test where the final grade depends on the weight of different assignments; if 80% of the class gets a 32 and 20% gets a 30, the average is pulled closer to 32.
WAM (Weighted Average Mass) = тИС(Mass├ЧFractional┬аAbundance)
Average┬аAtomic┬аMass=(Mass1тАЛ├ЧFraction1тАЛ)+(Mass2тАЛ├ЧFraction2тАЛ)
The principle relies on the relative abundance of isotopes. The formula calculates the sum of products of individual isotopic masses and their corresponding fractional abundances, where the sum of all fractional abundances must equal 1. This weighted sum accurately reflects the observed atomic mass of an element found in nature.
Isotopes are atoms of the same element with different neutron numbers.
Weighted average reflects the stability and distribution of isotopes in nature.
Fractional abundance is calculated by dividing the percentage by 100.
Accounts for the varying stability of isotopes in nature.
Essential for calculating accurate molar masses in chemical equations.
Does not represent the mass of a single atom, but an statistical average.
Calculation of molecular mass for compounds.
Radiometric dating using isotopic ratios.
Calculation: 30├Ч0.20+32├Ч0.80=6+25.6=31.6┬аu.
Option A is 31.2 u, which ignores the correct weighting. Option C is 30.8 u, which incorrectly weights the lighter isotope higher. Option D is 31.0 u, which assumes a simple arithmetic mean.
B is correct тАФ The weighted average calculation 30├Ч0.20+32├Ч0.80 results in 31.6┬аu.
Always ensure the fractional abundances add up to 1 (or 100%) before performing the multiplication to avoid common calculation errors.
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