Question

Given $4.6 \times {10^{22}}$ atoms of an element weigh $13.8g$. The atomic mass of the element is?
A. $290$
B. $180$
C. $34.4$
D. $104$

Answer 1

The number of atoms of an element and its weight have been given we will find the atomic mass by first multiplying the element’s weight with Avogadro number $\left( {{N_A}} \right)$and then divide it with the number of atoms present in the atom.
Complete answer:
Let us first know what Avogadro number is:
The Avogadro constant is a proportionality factor that connects the number of constituent particles in a sample to the amount of material present. ${N_A}{\text{ }} = {\text{ }}6.02214076 \times {10^{23}}mo{l^{ - 1}}$. Its SI unit is reciprocal of the mole.
We are aware that:
The mass (g) of an element in one mole is equal to its atomic weight.
An element's mole is equal to $6.022 \times {10^{23}}$atoms.
If an element has $4.6{\text{ }} \times {10^{22}}$atoms and weighs 13.8 g,
Then, that element's 6.023 x 1023 atoms will weigh:
$\dfrac{{6.023 \times 1023{\text{ }} \times 13.8{\text{ }}}}{{\left( {4.6{\text{ }} \times 1022} \right)}}g$
$\Rightarrow 180.69g$
The weight of one mole of an element is 180.69 g
Hence the element's atomic weight is 180.69 g.
Hence the correct answer to this question is 180.69g.

So, the correct answer is “Option B”.

Note:
There are $6.022 \times {10^{23}}$elementary entities in 1 mole, according to Avogadro's number. An atomic number (the number of protons equals the number of electrons) and an atomic weight can be ascribed to each atom (approximately equaling the number of protons plus the number of neutrons). The molecular weight of a material is equal to the mass of one mole of that substance.