Question

Question: The element silver (Ag) has two naturally occurring Isotopes ¹⁰⁹Ag. and with a mass of 109.905u. Silver consists of 51.82% and has an average atomic mass of ¹⁰⁷Ag107.868u. Calculate the mass of ¹⁰⁹Ag.

Short answer

Answer

The mass of ¹⁰⁹Ag is 108.904amu.

Step-by-step solution

Explanation of given data’s

$$\begin{gathered} \text{Mass of}{}_{}{}^{107}Ag=106.905amu \\ \text{Average atomic mass of silver}=107.868amu. \\ \text{Percent abundance of}{}_{}{}^{107}Ag\text{in silver = 51.82\%} \\ \text{Then the percent abundance of}{}_{}{}^{109}Ag\text{in silver =}(100-51.82)\%=48.18\% \end{gathered}$$

 Calculation of mass of  109Ag

$\text{Average mass}=(51.82\%ofA{g}^{107}Ag)$

Rearrange this equation to get our unknown value of¹⁰⁹Ag mass.

$$\begin{gathered} {}_{}{}^{109}Ag=\frac{\text{Average mass}-(51.82\%of{}_{}{}^{107}Ag)}{48.18\%} \\ {}_{}{}^{109}Ag=\frac{107.868amu-(0.5182\times 106.905amu)}{0.4818} \\ {}_{}{}^{109}Ag=108.904amu \end{gathered}$$

Hence, the mass of¹⁰⁹Ag isotope is 108.904amu.