N_A = 6.022 × 10²³ molecules/mol. Avogadro's law: equal volumes of gases at same T and P contain equal numbers of molecules. Universal gas constant R = N_A k.
-- NCERT Class 11 Physics, Ch. 12, p. 246Avogadro Number
8 MCQs6 revision cards9-step worked example
Source: NCERT Kinetic TheoryPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 25 Sep 2026
Avogadro Number, explained for NEET
Avogadro's number, Nₐ = 6.022 × 10²³ mol⁻¹, is the bridge between microscopic molecular quantities and macroscopic molar quantities. It tells you how many molecules (or atoms, ions, or particles) sit in exactly one mole of any substance.
Where it comes from in NCERT: Class 11 Physics Chapter 12 (Kinetic Theory), page 246 states this as a fundamental physical constant linking the gas constant R and the Boltzmann constant k through R = Nₐk. This relation is how the ideal gas law PV = nRT converts to PV = NkT, where N is the actual number of molecules.
The key relation to internalise:
Nₐ = R / k = 8.314 J mol⁻¹ K⁻¹ / 1.381 × 10⁻²³ J K⁻¹ ≈ 6.022 × 10²³ mol⁻¹
This means:
- n (moles) × Nₐ = N (number of molecules)
- Any per-mole quantity divided by Nₐ gives the per-molecule quantity (and vice versa)
Common confusions in NEET context:
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R vs k mix-up. R is per mole; k is per molecule. When a problem gives molecular-level data, use k. When it gives molar data, use R. Swapping them changes the answer by a factor of ~10²³.
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Forgetting the mole–molecule conversion. Problems sometimes give mass and ask for the number of molecules. You must go mass → moles (using molar mass M) → molecules (multiplying by Nₐ). Skipping the mole step is a direct route to a wrong option.
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Confusing Nₐ with N. Nₐ is a fixed constant. N is the actual number of molecules in a given sample, which depends on how many moles you have: N = nNₐ.
Watch-out: When a NEET stem says "number of molecules in 2 moles," the answer is 2 × 6.022 × 10²³ = 1.204 × 10²⁴ — not 6.022 × 10²³. Read whether the problem asks per mole or for the given sample.
Can you answer these Avogadro Number MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
Avogadro's number (Nₐ) represents:
Show answer and why every option is right or wrong
Answer: C. By definition, Avogadro's number is the number of constituent particles (atoms, molecules, ions) in one mole of any substance. This is stated in NCERT Class 11 Physics Chapter 12, page 246.
Why A is wrong: A is wrong as a definition. 1 g of hydrogen does contain about Nₐ atoms, because hydrogen's molar mass is about 1 g/mol, but that is a consequence of the mole for one element — and only approximate (1.008 g/mol) — not what Nₐ represents.
Why B is wrong: B describes a consequence (one mole of an ideal gas occupies 22.4 L at STP), but Nₐ is defined as particles per mole, not as particles per 22.4 L. The volume-based statement is a derived result, not the definition.
Why D is wrong: D is incorrect because the number of molecules in 1 kg depends on the molar mass of the substance, which varies. Nₐ is substance-independent — it is per mole, not per kilogram.
MCQ 2Easy RecallPractice
The Boltzmann constant k is related to Avogadro's number Nₐ and the gas constant R by:
Show answer and why every option is right or wrong
Answer: D. R = Nₐk, so k = R/Nₐ. This connects the per-mole gas constant to the per-molecule Boltzmann constant, as stated in NCERT Class 11 Physics Chapter 12, page 246.
Why A is wrong: A gives k = RNₐ, which would make k ≈ 5 × 10²⁴ J/K — absurdly large. The correct relation divides R by Nₐ, not multiplies.
Why B is wrong: B introduces an arbitrary R² term with no physical basis. The relation is linear: R = Nₐk.
Why C is wrong: C gives k = Nₐ/R ≈ 7.2 × 10²² K/J, which has the inverse of the right unit; k must have units J/K.
MCQ 3Easy RecallPractice
The numerical value of Avogadro's number is approximately:
Show answer and why every option is right or wrong
Answer: B. Nₐ = 6.022 × 10²³ mol⁻¹ is the standard accepted value, as referenced in NCERT Class 11 Physics Chapter 13.
Why A is wrong: A is off by a factor of 10³. This error arises from confusing the exponent — Nₐ is 10²³, not 10²⁶.
Why C is wrong: C is off by a factor of 10³ in the opposite direction. 10²⁰ is too small by three orders of magnitude.
Why D is wrong: D is the value of the Boltzmann constant k, not Avogadro's number. Students who confuse R/Nₐ with Nₐ itself may pick this.
MCQ 4Direct ApplicationPractice
How many molecules are present in 3.0 moles of an ideal gas?
Show answer and why every option is right or wrong
Answer: A. N = nNₐ = 3.0 × 6.022 × 10²³ = 1.806 × 10²⁴. The mole-to-molecule conversion requires multiplying the number of moles by Avogadro's number.
Why B is wrong: B is the number of molecules in one mole, not three. This answer forgets to multiply by n = 3.
Why C is wrong: C divides Nₐ by 3 instead of multiplying. The operation is N = n × Nₐ, not Nₐ / n.
Why D is wrong: D has the correct digits but wrong exponent (10²³ instead of 10²⁴). 3 × 6.022 = 18.06, which is 1.806 × 10¹ — shifting the exponent from 10²³ to 10²⁴.
MCQ 5Direct ApplicationPractice
The gas constant R = 8.314 J mol⁻¹ K⁻¹ and Avogadro's number Nₐ = 6.022 × 10²³ mol⁻¹. The Boltzmann constant k is:
Show answer and why every option is right or wrong
Answer: A. k = R/Nₐ = 8.314 / 6.022 × 10²³ = 1.381 × 10⁻²³ J K⁻¹. This is a direct application of the Nₐ = R/k relation from NCERT Class 11 Physics Chapter 12, page 246.
Why B is wrong: B has the correct coefficient but the wrong exponent (10⁻²¹ instead of 10⁻²³). This is an order-of-magnitude arithmetic slip during division by 10²³.
Why C is wrong: C gives R × Nₐ instead of R / Nₐ. Multiplying instead of dividing reverses the conversion direction entirely.
Why D is wrong: D simply appends 10²³ to R without dividing. k must be much smaller than R, not larger.
MCQ 6Direct ApplicationPractice
An ideal gas sample contains N = 1.204 × 10²⁴ molecules. The number of moles in the sample is:
Show answer and why every option is right or wrong
Answer: B. n = N/Nₐ = 1.204 × 10²⁴ / 6.022 × 10²³ = 2.0 mol. Converting molecules to moles requires dividing by Avogadro's number.
Why A is wrong: A gives n = 0.5, which inverts the division: Nₐ/N = 6.022 × 10²³/1.204 × 10²⁴ = 0.5. The number of moles is N/Nₐ.
Why C is wrong: C gives n = 1.0, which would mean N = Nₐ = 6.022 × 10²³. The given N is twice this value.
Why D is wrong: D confuses the Avogadro number's coefficient (6.022) with the mole count. The number 6.022 × 10²³ is Nₐ itself, not a mole value.
MCQ 7CalculationPractice
A container holds n moles of an ideal gas at pressure P and temperature T. If the gas constant is R and Avogadro's number is Nₐ, which expression correctly gives the number of molecules per unit volume?
Show answer and why every option is right or wrong
Answer: B. From PV = NkT, the number density N/V = P/(kT). This combines the ideal gas law with the molecular form (using k = R/Nₐ). Both steps — writing the molecular form and isolating N/V — are required.
Why A is wrong: A incorrectly multiplies by P. From PV = nRT, n/V = P/(RT), so N/V = nNₐ/V = NₐP/(RT). Option A has an extra factor of n, making it dimensionally inconsistent.
Why C is wrong: C gives nR/(NₐT), which equals nkT⁻¹ — this is missing the pressure entirely and has wrong dimensions for number density (should be m⁻³).
Why D is wrong: D gives PNₐ/R, which has units Pa·K/J = K·m⁻³ — not a number density (m⁻³). It omits the temperature dependence entirely.
MCQ 8Concept TrapPractice
Two ideal gas samples — one containing helium (M = 4 g/mol) and the other nitrogen (M = 28 g/mol) — each have exactly one mole at the same temperature. Which statement about the number of molecules in each sample is correct?
Show answer and why every option is right or wrong
Answer: C. One mole of any substance contains exactly Nₐ molecules, regardless of molar mass. Molar mass determines the mass of one mole, not the number of particles in it. This is the core meaning of Avogadro's number.
Why A is wrong: A confuses mass with molecule count. Lighter molar mass means less mass per mole, not more molecules per mole. One mole always contains Nₐ particles.
Why B is wrong: B makes the same error in reverse — heavier molar mass means more mass per mole, but the molecule count per mole is still Nₐ.
Why D is wrong: D is incorrect. The number of molecules in one mole is Nₐ by definition. R connects to Nₐ through k = R/Nₐ, but the molecule count is fixed by the mole definition, not by R.
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Avogadro Number: quick recall before you leave
How do you solve a Avogadro Number question? A worked example
- 1
Given
• R = 8.314 J mol⁻¹ K⁻¹• k = 1.381 × 10⁻²³ J K⁻¹• n = 5.0 mol
- 2
Required
(a) Avogadro's number Nₐ
(b) Total molecules N in 5.0 moles - 3
Concept
Avogadro's number bridges the molar scale (R) and the molecular scale (k). From R = Nₐk, we extract Nₐ. Then N = nNₐ converts moles to molecules.
- 4
Formula
(a) Nₐ = R / k
(b) N = nNₐ - 5
Substitution
(a) Nₐ = 8.314 / 1.381 × 10⁻²³
(b) N = 5.0 × Nₐ - 6
Calculation
(a) Nₐ = (8.314 / 1.381) × 10²³ = 6.021 × 10²³ mol⁻¹
(Rounding: 8.314 / 1.381 = 6.0203… ≈ 6.021 to 4 significant figures, matching the precision of the given data.)
(b) N = 5.0 × 6.022 × 10²³ = 3.011 × 10²⁴
Note on exact values: the factor 5.0 is a given counting quantity in this problem context and does not limit significant figures. The answer precision is governed by Nₐ (4 sig figs). - 7
Final answer
(a) Nₐ ≈ 6.021 × 10²³ mol⁻¹ — which is the accepted 6.022 × 10²³ to three significant figures. The fourth digit differs because R and k are themselves quoted to four figures here; do not read the difference as an error in either.
(b) N = 3.011 × 10²⁴ molecules - 8
Common trap
Confusing R and k: using k in place of R (or vice versa) changes the answer by ~10²³. If you get a Nₐ on the order of 10⁰ or 10⁴⁶, you have swapped R and k.
- 9
Similar NEET-style question
"The Boltzmann constant is 1.38 × 10⁻²³ J K⁻¹ and R = 8.31 J mol⁻¹ K⁻¹. How many molecules are present in 0.50 moles of oxygen at STP?"
(Answer: N = 0.50 × (8.31/1.38 × 10⁻²³) ≈ 0.50 × 6.02 × 10²³ = 3.01 × 10²³.)
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What to remember before solving Avogadro Number questions
More in Kinetic Theory: 2 exam traps and mistakes · 5 formulas · 4 question patterns from its other lessons.
Avogadro Number questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
15.6 m³
25.6 × 10⁶ m³
35.6 × 10³ m³
45.6 × 10⁻³ m³
NTA Answer: Option 1(final)
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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