Question

Which among the following has the largest number of atoms?
[A] 0.5g atom of Cu
[B] 0.635g of Cu
[C] 0.25 mol of Cu atom
[D] 1g of Cu

Answer 1

Hint: To find the number of atoms in any case remember that-
The molar mass (g) of any molecule contains $N_A$number of atoms of that molecule. Also, each mole contains $N_A$number of atoms. So, the number of atoms in gm or in moles can be calculated easily.

Complete step by step solution:
We know, the molar mass of Cu is 63.5g
I.e. 63.5g of copper contains Avogadro’s number ($N_A$) atoms of copper
$\therefore$63.5g copper= $6.023\times {10}^{23}$atoms of copper.
So, following unitary method, we get-
0.635g of copper=$(6.023\times {10}^{23}\times 0.635)÷63.5$atoms of copper= $6.023\times {10}^{21}$atoms of copper
Similarly, for 1g of copper we have,
1g of copper= $(6.023\times {10}^{23}\times 1)÷63.5$=$9.485\times {10}^{21}$atoms of copper
For 0.5g atom of Cu,
Number of atoms= $0.5\times 6.022\times {10}^{23}$= $3.011\times {10}^{23}$atoms of copper
Now, for 0.25 moles of copper,
$\because$1 mole of copper= $6.023\times {10}^{23}$atoms of copper
$\therefore$0.25 moles of copper= $0.25\times 6.023\times {10}^{23}$=$1.50575\times {10}^{23}$atoms of copper.
From the above calculations it is clear that 0.5g atom of Copper has the highest number of atoms present.
Therefore, option [A] 0.5g atom of Cu atom is the correct answer.

ADDITIONAL INFORMATION:
According to Avogadro’s Law, 1 mole of every gas occupies 22.4 litres of volume at STP ($0^{\circ }$C temperature and 1atm pressure) and contains Avogadro’s number$6.023\times {10}^{23}$ of particles.

NOTE: It is important here to remember the value of the Avogadro’s number and also the molar mass of copper, the rest can be calculated easily. Also note that in option [A] the unit it g atom
g atom= 1 mole = $N_A$atoms.
Whereas, in options [B] and [D] the unit is in grams so we have to divide it by the molar mass. And again option [C] is in mole units so it will be simply multiplied to the Avogadro’s number.