Respuesta :
Answer:
The percent compositions of the first isotope = 47.78 %
The percent compositions of the second isotope = 100 - 47.78 % = 52.22 %
Explanation:
The formula for the calculation of the average atomic mass is:
[tex]Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})[/tex]
Given that:
Since the element has only 2 isotopes, so the let the percentage of first be x and the second is 100 -x.
For first isotope :
% = x %
Mass = 150.920 u
For second isotope :
% = 100 - x
Let, Mass = 152.921 u
Given, Average Mass = 151.965 u
Thus,
[tex]151.965=\frac{x}{100}\times {150.920}+\frac{100-x}{100}\times {152.921}[/tex]
[tex]150.92x+152.921\left(100-x\right)=15196.5[/tex]
[tex]-2.001x=-95.6[/tex]
Solving for x, we get that:
x=47.78 %
The percent compositions of the first isotope = 47.78 %
The percent compositions of the second isotope = 100 - 47.78 % = 52.22 %
