Moseley's Law
Atomic number is nuclear charge.
Lesson at a glanceShow the key points
- √ν = a(Z − b) (44.2); b ≈ 1 for Kα.
- Bohr with one screening K electron: ν = (3Rc/4)(Z − 1)², a = √(3Rc/4).
- Elements are ordered by Z (cobalt 27, nickel 28), not atomic weight.
In 1913 a 26-year-old physicist measured the Kα lines of a long row of elements and found one simple straight line. It showed that an element’s identity is its nuclear charge, not its mass, and it put the periodic table on firm ground.
The pattern
Henry Moseley used crystals to measure the wavelengths of the characteristic X-rays from many different targets. Plotting the square root of the Kα frequency against the element’s position in the periodic table, the atomic number Z, gave a straight line:
Why the line is straight: Bohr’s model
For a single electron around a nucleus of charge Ze, Bohr’s model gives the photon frequency for a jump from n = 2 to n = 1 as ν = (3/4)RcZ². Now think of a heavy atom with one K electron missing. An L electron about to drop in sees the nucleus (+Ze) partly shielded by the one K electron still there, so it feels an effective charge of about (Z − 1)e. Replacing Z by Z − 1:
What it did for the periodic table
Before Moseley, elements were ordered by atomic weight, with a few awkward exceptions where chemistry demanded a swap. Moseley’s law showed that the real ordering number is Z, the charge of the nucleus:
- Cobalt and nickel: cobalt (atomic weight 58.93) is heavier than nickel (58.69), so ordering by weight put nickel first. Their X-ray lines put cobalt at Z = 27 and nickel at Z = 28, matching their chemistry.
- Gaps: missing points on the line revealed elements not yet discovered, at Z = 43, 61, 72 and 75. All of them were later found (technetium, promethium, hafnium, rhenium).
X-ray lines are now a standard way to identify which elements are present in a sample: X-ray fluorescence analysis.
The Kα wavelengths of copper (Z = 29) and molybdenum (Z = 42) are 154.1 pm and 70.9 pm. Find a and b in √ν = a(Z − b).
Using a = 4.97 × 10⁷ Hz½ and b = 1, estimate the Kα wavelength of iron (Z = 26).
- 1Moseley's law: √ν = a(Z − b) for a given characteristic line; b ≈ 1 for Kα.
- 2Bohr's model with the nucleus screened by one K electron gives ν = (3Rc/4)(Z − 1)², so a = √(3Rc/4).
- 3Elements are ordered by nuclear charge Z, not atomic weight (cobalt 27 before nickel 28).
- 4Gaps on the line predicted undiscovered elements; X-ray lines identify elements in a sample.
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