Answer: 67%
Explanation: The weighted averages of the two isotopes must add to 131.01. Let Y be the percentage of isotope 129. Then (1-Y) will be the percentage of isotope 132. The weighted average of each is:
129: 129Y
132: 132(1-Y)
Their sum is equal to 131.01
129Y + 132(1-Y) = 131.01
Y = 0.33, or 33%
(1-Y) = 0.67, or 67%
Check: 129*(0.33) = 42.57
132*(0.67) = 88.44
Sum = 131.01 It checks OK The 132 isotopes is 67% of the sample.
Considering the definition of atomic mass, isotopes and atomic mass of an element, the percent abundance of ¹³²X is 67%.
First of all, the atomic mass (A) is obtained by adding the number of protons and neutrons in a given nucleus of a chemical element.
The same chemical element can be made up of different atoms, that is, their atomic numbers are the same, but the number of neutrons is different. These atoms are called isotopes of the element.
On the other hand, the atomic mass of an element is the weighted average mass of its natural isotopes. In other words, the atomic masses of chemical elements are usually calculated as the weighted average of the masses of the different isotopes of each element, taking into account the relative abundance of each of them.
In this case, you know:
Then, the average mass of X can be calculated as:
132 amu×y + 129 amu×( 1-y)= 131.01 amu
Solving, you can find the percent abundance of ¹³²X:
132 amu×y + 129 amu×1 - 129 amu×y= 131.01 amu
132 amu×y + 129 amu - 129 amu×y= 131.01 amu
132 amu×y - 129 amu×y= 131.01 amu - 129 amu
3 amu×y= 2.01 amu
y= 2.01 amu÷ 3 amu
y= 0.67= 67%
Finally, the percent abundance of ¹³²X is 67%.
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