Question

The average atomic mass of Eu is 151.96 amu. There are only two naturally occurring isotopes of europium, Eu with a mass of 151.0 amu and Eu with a mass of 153.0 amu. The natural abundance of the Eu isotope must be approximately

Answer 1

Answer:

The percentage abundance of Eu isotopes are 52 %  and 48 % .

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 = 151.0 amu

For second isotope :

% = 100  - x  

Mass = 153.0 amu

Given, Average Mass = 151.96 amu

Thus,

$151.96=\frac{x}{100}\times {151.0}+\frac{100-x}{100}\times {153.0}$

Solving for x, we get that:

x = 52 %

Thus percentage abundance of Eu isotopes are 52 %  and 48 % .