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Question: Mass of a single atom of silver is \[1.794 \times {10^{ - 22}}\]. What is the atomic mass of silver?...

Mass of a single atom of silver is 1.794×10−221.794 \times {10^{ - 22}}. What is the atomic mass of silver?

Explanation

Solution

For this we must know the definition of atomic mass unit. We must know the number of atoms present in a certain atomic mass of an element which is given by Avogadro’s number.

Complete step by step solution:
Since we have to calculate the atomic mass of silver, let us assume that the atomic mass of silver is x grams.
Avogadro number gives us the value of the number of atoms, molecules or ions present in one mole of a given species. The value of Avogadro number or Avogadro constant is 6.022×10236.022 \times {10^{23}}. Mole is a unit to determine the amount of substance. 1 mole = 6.022 × 1023 molecules1{\text{ mole = 6}}{\text{.022 }} \times {\text{ 1}}{{\text{0}}^{23}}{\text{ molecules}}.
For example one mole of carbon atom contains 6.022×10236.022 \times {10^{23}} carbon atoms. Similarly one mole of Na+{\text{N}}{{\text{a}}^ + } ion will contain 6.022×10236.022 \times {10^{23}} number of ions.
Similarly 1 mole of silver will have 6.022×10236.022 \times {10^{23}} moles of silver atoms. Hence
Mass of one mole of silver =mass of 6.022×1023 silver atoms = {\text{mass of }}6.022 \times {10^{23}}{\text{ silver atoms}}. Mass of one mole of silver will be the atomic mass of silver. Hence according to this,
atomic mass of silver=mass of 6.022×1023 silver atoms{\text{atomic mass of silver}} = {\text{mass of }}6.022 \times {10^{23}}{\text{ silver atoms}}.
Mass of one atom of silver is given to us that is 1.794×10−221.794 \times {10^{ - 22}}.
mass of 6.022×1023 atoms of silver = 6.022×1023×1.794×10−22=108 atomic mass unit{\text{mass of }}6.022 \times {10^{23}}{\text{ atoms of silver = }}6.022 \times {10^{23}} \times 1.794 \times {10^{ - 22}} = 108{\text{ atomic mass unit}}
Hence the atomic mass of silver is 108 u or amu.

Hence the atomic mass of silver is 108 u or amu.

Note:
As we have seen that atomic mass unit is a very small unit so instead of that we use moles as a unit. It is a unit to determine the amount of substance. 1 mole = 6.022 × 1023 molecules1{\text{ mole = 6}}{\text{.022 }} \times {\text{ 1}}{{\text{0}}^{23}}{\text{ molecules}}. Silver is a d block element and is very soft, ductile and malleable. It is extensively used in photography, catalysis and nanoparticles study.