Question

The element silver (Ag) has two naturally occurring isotopes: 109Ag and 107Ag with a mass of 106.905 amu. Silver consists of 51.82 % Ag and has an average atomic mass of 107.868 amu. Calculate the mass of 109Ag

Answer 1

Answer:

108.76 amu is the mass of 109Ag

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, 109Ag:

% = 51.82 %

Mass = x amu

For second isotope, 107Ag:

% = 100  - x   = 100 - 51.82 % = 48.18 %

Mass = 106.905 amu

Given, Average Mass = 107.868 amu

Thus,  

$107.868=\frac{51.82}{100}\times {x}+\frac{48.18}{100}\times {106.905}$

Solving for x, we get that:

x = 108.76 amu

108.76 amu is the mass of 109Ag