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Multiple Choice
Bromine has two naturally occurring isotopes, Br-79 and Br-81, with an atomic mass of 79.904 amu. Given that the mass of Br-81 is 80.9163 amu and its natural abundance is 49.31%, what is the mass and natural abundance of Br-79?
A
Mass: 78.918 amu, Abundance: 49.31%
B
Mass: 78.918 amu, Abundance: 50.69%
C
Mass: 80.9163 amu, Abundance: 50.69%
D
Mass: 80.9163 amu, Abundance: 49.31%
Verified step by step guidance
1
Understand that the average atomic mass of bromine is given as 79.904 amu, which is a weighted average of the masses of its isotopes based on their natural abundances.
Let the mass of Br-79 be denoted as \( m_{79} \) and its natural abundance as \( a_{79} \). The mass of Br-81 is given as 80.9163 amu with a natural abundance of 49.31%.
Set up the equation for the average atomic mass: \( 79.904 = m_{79} \times a_{79} + 80.9163 \times 0.4931 \).
Since the total abundance of all isotopes must equal 100%, express \( a_{79} \) as \( 1 - 0.4931 \) (since \( a_{81} = 0.4931 \)).
Substitute \( a_{79} = 0.5069 \) into the equation and solve for \( m_{79} \) using the average atomic mass equation: \( 79.904 = m_{79} \times 0.5069 + 80.9163 \times 0.4931 \).