Respuesta :
There are two naturally occurring isotopes of gallium: mass of Ga-69 isotope is 68.9256 amu and its percentage abundance is 60.11%, let the mass of other isotope that is Ga-71 be X, the percentage abundance can be calculated as:
%Ga-71=100-60.11=39.89%
Atomic mass of an element is calculated by taking sum of atomic masses of its isotopes multiplied by their percentage abundance.
Thus, in this case:
Atomic mass= m(Ga-69)×%(Ga-69)+X×%(Ga-71)
From the periodic table, atomic mass of Ga is 69.723 amu.
Putting the values,
[tex]69.723 amu=(68.9256 amu)(\frac{60.11}{100})+X(\frac{39.89}{100})[/tex]
Thus,
[tex]69.723 amu=41.4312 amu+X(\frac{39.89}{100})[/tex]
Rearranging,
[tex]X=\frac{69.723 amu-41.4312 amu}{0.3989}=70.9246 amu[/tex]
Therefore, mass of Ga-71 isotope is 70.9246 amu.
Answer: The atomic mass of gallium-71 is 70.92 amu.
Explanation:
Mass of isotope Ga-69 = 68.9256 amu
% abundance of isotope Ga-69 = 60.11% = [tex]\frac{60.11}{100}=0.6011[/tex]
Mass of isotope Ga-71 = ?
% abundance of isotope Ga-71 = (100-60.11)% = [tex]\frac{39.89}{100}=0.3989[/tex]
Formula used for average atomic mass of an element :
[tex]\text{ Average atomic mass of an element}=\sum(\text{atomic mass of an isotopes}\times {{\text { fractional abundance}})[/tex]
[tex]\text{ Average atomic mass of an element}=69.723amu[/tex]
[tex]69.723 =\sum[(68.9256\times 0.6011)+(x\times 0.3989)][/tex]
[tex]x=70.92amu[/tex]
Therefore, the atomic mass of gallium-71 is 70.92 amu.
