Q.The number of atoms present in one mole of an element is equal to Avogadro number. Which of the following element contains the greatest number of atoms?

Concept: Molecular Mass Calculation and Avogadro's Number

The number of atoms in a sample equals the number of moles multiplied by Avogadro's number ($N_A = 6.022 \times 10^{23}$). To find which sample has the most atoms, we calculate moles using $n = \frac{\text{mass}}{\text{molar mass}}$ for each option.

Step 1: Calculate moles for each element:

• (i) He: $n = \frac{4}{4} = 1$ mol
• (ii) Na: $n = \frac{46}{23} = 2$ mol
• (iii) Ca: $n = \frac{0.40}{40} = 0.01$ mol
• (iv) He: $n = \frac{12}{4} = 3$ mol …

The question tests whether you can connect mass, molar mass, and the mole concept. Avogadro's number $N_A \approx 6.022 \times 10^{23}$ tells us how many particles (atoms, in this case) are in one mole. Since every element here exists as individual atoms (not molecules), the number of atoms is simply the number of moles multiplied by $N_A$.

The strategy is straightforward: calculate the number of moles for each option, then compare. Whichever has the most moles automatically has the most atoms.

Now let's work through each option systematically.

1. Option (i): 4 g He

Helium has a molar mass of 4 g/mol (atomic mass ≈ 4 u).

Number of atoms = $1 \times N_A = N_A$

2. Option (ii): 46 g Na

Sodium has a molar mass of 23 g/mol (atomic mass ≈ 23 u).

Number of atoms = $2 \times N_A = 2N_A$

3. Option (iii): 0.40 g Ca

Calcium has a molar mass of 40 g/mol (atomic mass ≈ 40 u).

$n_{\text{Ca}} = \frac{0.40}{40} = 0.01 \text{ mol}$ …

Concept: Mole Concept & Avogadro's Number

The number of atoms in a given mass of an element depends on:

• The mass of the sample
• The molar mass (atomic mass) of the element

Since one mole of any element contains the same number of atoms (Avogadro number, $6.022 \times 10^{23}$), the element with the largest number of moles will have the greatest number of atoms.

Method: Mole Comparison Method

Steps:

1. Write the formula for number of moles:

2. Find molar masses (from periodic table):

   • He: $4 \, \text{g/mol}$
   • Na: $23 \, \text{g/mol}$
   • Ca: $40 \, \text{g/mol}$

3. Calculate moles for each option:

   • (i) 4 g He

• (ii) 46 g Na

• (iii) 0.40 g Ca $\text{Moles} = \frac{0.40}{40} = 0.01 \text{ mole}$ …

🧠 The Core Concept

The number of atoms in a sample is given by:

where $N_A$ is Avogadro’s number ($6.022 \times 10^{23}$).

So, more moles → more atoms (since $N_A$ is constant).

✗ Mistake #1: Comparing mass directly instead of moles

What students do:

They see 46 g Na vs 4 g He and think “46 > 4, so Na has more atoms.”

Why it’s wrong:

Mass alone doesn’t tell you the number of atoms — you must convert to moles using molar mass.

How to avoid:

Always convert mass to moles first:

Then compare moles.

✗ Mistake #2: Forgetting that He is monatomic

What students do:

They treat He like a diatomic gas (e.g., O₂, N₂) and think “1 mole of He = 2 moles of atoms.”

Why it’s wrong:

Helium is a noble gas — it exists as single atoms. So 1 mole of He = 1 mole of He atoms.

How to avoid:

Memorise:

• Monatomic gases (noble gases: He, Ne, Ar, etc.) → 1 atom per particle
• Diatomic gases (H₂, O₂, N₂, F₂, Cl₂) → 2 atoms per particle

✗ Mistake #3: Using atomic mass in grams instead of g/mol

What students do:

They write “4 g He = 4 moles” because atomic mass of He = 4 u, but they forget the unit is g/mol.

Why it’s wrong:

Atomic mass = 4 u means molar mass = 4 g/mol, not “4 g = 4 moles.”

How to avoid:

Always write the unit:

• Molar mass of He = 4 g/mol
• Molar mass of Na = 23 g/mol
• Molar mass of Ca = 40 g/mol

Then: …