Noesis
1.4.2Periodic Table — First Look

Modern periodic law — based on atomic number

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🇮🇳 Yeh note Hinglish mein padho →

WHAT is the Modern Periodic Law?

The key change from the older idea:

  • Mendeleev's law (old): properties are a periodic function of atomic mass.
  • Modern law (Moseley, 1913): properties are a periodic function of atomic number.

WHY atomic number and not atomic mass?

The three famous anomalies (mass says one order, chemistry says the opposite):

Pair Atomic mass order Chemistry demands Fixed by ZZ?
Ar (39.9) vs K (39.1) K should come first (lighter) Ar with noble gases, K with alkali ✅ ZAr=18<ZK=19Z_{Ar}=18 < Z_K=19
Co (58.9) vs Ni (58.7) Ni should come first Co before Ni ✅ ZCo=27<ZNi=28Z_{Co}=27 < Z_{Ni}=28
Te (127.6) vs I (126.9) I should come first Te before I ✅ ZTe=52<ZI=53Z_{Te}=52 < Z_I=53

HOW did Moseley prove ZZ is the right basis?

Deriving Moseley's law from scratch

Step 1 — Why any relation at all? An X-ray is emitted when an inner electron drops to a lower shell. Its frequency depends on how strongly the nucleus pulls electrons — i.e. on nuclear charge.

Why this step? Nuclear charge = number of protons = ZZ. So X-ray frequency should encode ZZ.

Step 2 — Bohr-type energy of a transition. For a one-electron-like transition, energy ∝(effective nuclear charge)2\propto (\text{effective nuclear charge})^2. Writing effective charge as (Z−σ)(Z - \sigma) where σ\sigma is a screening constant: hν∝(Z−σ)2h\nu \propto (Z-\sigma)^2

Why this step? Inner electrons partly shield the nucleus, so the felt charge is Z−σZ-\sigma, not ZZ.

Step 3 — Take the square root (frequency itself is what's measured): ν=a (Z−σ)\sqrt{\nu} = a\,(Z - \sigma)

Figure — Modern periodic law — based on atomic number

Step 4 — Why this settled the debate. ν\sqrt{\nu} vs ZZ gives a perfect straight line, while ν\sqrt{\nu} vs atomic mass does NOT. So ZZ — not mass — is the atom's true, ordering identity.

Worked Examples

Common Mistakes

Recall Feynman: explain to a 12-year-old

Imagine kids standing in a line by how many candies (== protons) they have — 1 candy, 2 candies, 3 candies... As you walk down the line, you notice every so often a kid loves sharing (like the sharing kids repeat at positions 3, 11, 19...), then some loners who never share (positions 2, 10, 18...). The pattern repeats as the candy count goes up. That's the periodic law: line them up by candy count (atomic number), and their behaviour repeats. Earlier people lined them by weight — but weight sometimes lied (a fatter kid could actually have fewer candies), so a scientist named Moseley zapped each atom with X-rays to count the real candies, and everyone fell into perfect order.

Active Recall

State the Modern Periodic Law.
Physical and chemical properties of elements are a periodic function of their atomic number (ZZ).
On what basis did Mendeleev arrange elements?
Atomic mass.
Who established that atomic number is the fundamental property?
Henry Moseley (1913), via X-ray frequency experiments.
Write Moseley's law.
ν=a(Z−b)\sqrt{\nu} = a(Z - b), where ν\nu is characteristic X-ray frequency, ZZ atomic number, a,ba,b constants.
A plot of ν\sqrt{\nu} vs ZZ gives what shape, and what does it prove?
A straight line; proves ZZ is a fundamental integer property that orders elements.
Why is Ar placed before K despite being heavier?
Because ZAr=18<ZK=19Z_{Ar}=18 < Z_K=19; the modern law orders by atomic number, not mass.
Name the three anomalous pairs solved by using ZZ.
Ar–K, Co–Ni, Te–I.
What does the constant bb in Moseley's law physically represent?
The screening (shielding) constant σ\sigma — inner electrons reduce the effective nuclear charge to (Z−b)(Z-b).
"Periodic function" means
properties repeat in a regular cycle as ZZ increases.

Connections

Concept Map

orders elements

properties are

replaced by

caused

examples

automatically fixes

established basis of

measured

encodes nuclear charge

square root gives

proves

Atomic number Z = protons

Modern Periodic Law

Periodic function of Z

Mendeleev law - atomic mass

Mass-order anomalies

Ar-K, Co-Ni, Te-I

Moseley X-ray experiment 1913

X-ray frequency v

Effective charge Z minus sigma

Moseley's Law: sqrt v = a Z minus b

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, purane zamane mein Mendeleev ne elements ko unke atomic mass ke hisaab se line mein lagaya tha. Lekin kuch jagah masla aa gaya — jaise Argon ka mass Potassium se zyada hai, phir bhi chemistry keh rahi thi ki Argon pehle aana chahiye (kyunki Ar noble gas hai, K alkali metal). Mendeleev ko ye elements manually swap karne pade, bina kisi reason ke. Yahi cheez batati hai ki mass sahi base nahi tha.

Phir aaya Moseley (1913). Usne har element pe X-rays maari aur nikalne wali X-ray ki frequency (ν\nu) naapi. Usne dekha ki ν\sqrt{\nu} aur atomic number ZZ (yaani protons ki ginti) ke beech ek perfect straight line banti hai: ν=a(Z−b)\sqrt{\nu}=a(Z-b). Matlab ZZ hi asli, fundamental property hai jo har element ko unique banati hai — mass nahi.

Isi se bana Modern Periodic Law: "Elements ki physical aur chemical properties unke atomic number ka ek periodic function hain." Periodic function ka matlab — jaise-jaise ZZ badhta hai (1,2,3…1,2,3\dots), properties baar-baar repeat hoti hain, wallpaper ke pattern ki tarah. Aur best baat — Ar/K, Co/Ni, Te/I wale saare purane exceptions ab automatically theek ho jaate hain, kyunki ZZ se order karne pe sab apni sahi jagah baith jaate hain.

Yaad rakhne ka trick: "Mendeleev Measured Mass, Moseley Marked Number." Exam mein agar poochha "modern law kis pe based hai?" — jawab hamesha atomic number (ZZ), kabhi mass nahi.

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Connections

Mendeleev's periodic table — based on atomic massChemistry · 1.4.1Explain atomic number and mass numberBiology · 1.2.2Effective nuclear charge Z_eff — Slater's rulesChemistry · 2.2.1Bohr model of hydrogen — postulates, radius rₙ = 0.529 n² - Z Å, energy Eₙ = −13.6 Z² - n² eVChemistry · 1.2.7Mendeleev's periodic table — based on atomic massChemistry · 1.4.1