Question

Calculate the weight of one atom of $Ag$ . (Atomic weight of $Ag = 108$ )
(A) $17.93 \times {10^{ - 23}}{\text{gm}}$
(B) $16.93 \times {10^{ - 23}}{\text{gm}}$
(C) $17.93 \times {10^{23}}{\text{gm}}$
(D) $36 \times {10^{ - 23}}{\text{gm}}$

Answer 1

A convenient method of expressing the quantity of a substance is the mole concept. It is possible to break down any measurement into two parts: the numerical magnitude and the units in which the magnitude is expressed. We will solve this question by using the basic theory of mole concept.

Formula Used
In a given pure sample, the number of moles of a substance can be represented by the following formula:
$n = \dfrac{N}{{{N_A}}}$
Where
$n$ is the number of moles
${N_A}$ is the Avogadro’s constant
$N$ is the total number of elementary entities.

Complete Step-by-Step solution
One mole of any entity is defined as the quantity of a substance containing exactly $6.023 \times {10^{23}}$ 'elementary entities' of the substance given.
So, one mole of any substance will be equal to $6.023 \times {10^{23}}$ entities.
Now, we know that one mole atoms of $Ag$ weighs $108{\text{g}}$
That is,
Weight of $6.023 \times {10^{ - 23}}$ atoms of $Ag = 108{\text{g}}$
Then, the weight of one atom of $Ag$ will be given by
$\dfrac{{108}}{{6.023 \times {{10}^{ - 23}}}}$
Upon solving, we get
Weight of $1$ atom of $Ag = 17.93 \times {10^{ - 23}}{\text{g}}$
Hence, the correct option is (A).

Additional Information
The German chemist Wilhelm Ostwald introduced the word "mole" around the year $1896$ deriving the term from the Latin word moles, meaning a 'heap' or 'pile. It is not always possible for the number of moles of a molecule to be equal to the number of moles of its constituent elements. A mole is the unit of measurement in the International System of Units for the quantity of substances.

Note
The number $6.023 \times {10^{23}}$ is commonly referred to as the constant of Avogadro and is often denoted by the ' ${N_A}$ ' symbol. Atoms, molecules, monatomic/polyatomic ions, and other particles can be the fundamental entities that can be represented in moles (such as electrons).