Question

Europium has two isotopes. One of the isotopes has a mass of 150.920 amu, and the other has a mass of 152.921 amu. Europium has an atomic mass of 151.965 amu. What are the percent compositions of the two isotopes

Answer 1

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:

$Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})$

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,  

$151.965=\frac{x}{100}\times {150.920}+\frac{100-x}{100}\times {152.921}$

$150.92x+152.921\left(100-x\right)=15196.5$

$-2.001x=-95.6$

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 %