Question

What is the average atomic mass of silver if 13 out of 25 atoms are silver – 107 and 12 out of 25 atoms are silver – 109?

Answer 1

Hint: Isotope is the property of any element to have the same atomic number but different mass numbers. For calculating the mass numbers of isotopes, an average atomic mass is used, that takes the average of the mass of each isotopic form. Silver has isotopes of Ag – 107, and Ag – 109 mass.

Complete answer:
Isotopes of an element are the forms of the same element that have the same atomic number but they differ in their mass number. So, average atomic mass is used to calculate their atomic masses.
We have been given isotopes of silver, with their atoms that are in abundance. We have to calculate the atomic mass of silver, given that 13 out of 25 atoms are silver – 107 and 12 out of 25 atoms are silver – 109.
The formula used is, average atomic mass = $\sum\limits_{i}{(isotop{{e}_{i}}\times abundanc{{e}_{i}})}$
For silver – 107, the abundance will be $\dfrac{13}{25}$ , and for silver – 109, it will be $\dfrac{12}{25}$ , so the average atomic mass is calculated as,
Average atomic mass = $107\,u\,\times \dfrac{13}{25}+109\,u\,\times \dfrac{12}{25}$
Therefore, average atomic mass = 107.96 u
Hence, the average atomic mass of silver if 13 out of 25 atoms are silver – 107 and 12 out of 25 atoms are silver – 109 is 107.96 u

Note:
The property of an element to have different isotopes is used in the phenomena of radioactivity. The isotopes in abundance are either their percentage divided by hundred, or their number of atoms upon total number of atoms present. This is because each isotope will contribute its part by its total abundance.