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X-ray questions in JEE Advanced usually ask one of three things: the shortest wavelength a tube can produce, the wavelength of a characteristic line, or which element made a given line. All three come from two simple ideas. This post covers both, with worked examples checked against measured data.
Which exams include X-rays and Moseley's law?
The JEE (Advanced) 2026 syllabus lists "Characteristic and continuous X-rays, Moseley's law" under modern physics. The JEE (Main) 2026 syllabus mentions X-rays only as part of the electromagnetic spectrum. In school, Moseley appears in the NCERT Class 11 chemistry chapter on classification of elements. Check the syllabus for your exam year.
How does an X-ray tube work?
Electrons are accelerated through a potential difference V and hit a metal target. Two things happen.
Continuous X-rays. As electrons slow down in the target, they emit radiation over a range of wavelengths. An electron cannot give a photon more energy than it has, eV, so there is a sharp lower limit on the wavelength: λ_min = hc/(eV).
Characteristic X-rays. A fast electron can knock out an electron from an inner shell of a target atom. When an outer electron drops into the hole, the atom emits a photon of a definite energy. These sharp lines depend on the target element, not on V. The Kα line comes from an electron dropping from the L shell (n = 2) to the K shell (n = 1).
Wilhelm Röntgen discovered X-rays and received the first Nobel Prize in Physics in 1901. Our profile of Wilhelm Röntgen tells that story.
Worked example 1: cut-off wavelength
A tube runs at 30 kV. Using hc = 1240 eV nm, λ_min = 1240 eV nm / 30,000 eV = 0.0413 nm.
Double the voltage and λ_min halves. The characteristic lines stay where they are.
What is Moseley's law?
In 1913 Henry Moseley measured the characteristic X-ray lines of many elements in The high-frequency spectra of the elements, followed by a second part in 1914. NCERT summarises the result: a plot of the square root of the X-ray frequency against atomic number Z gave a straight line, while a plot against atomic mass did not. Moseley "thereby showed that the atomic number is a more fundamental property of an element than its atomic mass", and the periodic law was restated in terms of atomic number.
In symbols, √ν = a(Z − b), where a and b are constants for a given line. For Kα, a Bohr-model estimate gives a handy form. An L-shell electron sees the nuclear charge screened by the one remaining K-shell electron, so the effective charge is about (Z − 1). Using the hydrogen energy levels from our post on Bohr model and hydrogen spectrum problems:
E(Kα) ≈ 13.6 eV × (Z − 1)² × (1/1² − 1/2²) = 10.2 eV × (Z − 1)²
Worked example 2: the Kα line of copper
Copper has Z = 29.
E ≈ 10.2 × (29 − 1)² = 10.2 × 784 = 8.00 × 10³ eV.
λ = 1240 / 8000 nm = 0.155 nm.
The X-Ray Data Booklet from Lawrence Berkeley National Laboratory lists copper's Kα₁ line at 8,047.78 eV, a wavelength of 0.154 nm. The simple estimate is within about 1%. For iron (Z = 26) it gives 6,375 eV against a measured 6,403.84 eV.
Worked example 3: which element is it?
A target gives a Kα line at 6,930 eV. Find Z.
(Z − 1)² = 6930 / 10.2 = 679, so Z − 1 = 26.1 and Z ≈ 27. That is cobalt, and the data booklet lists cobalt's Kα₁ line at 6,930.32 eV.
This is how Moseley's method could check the order of elements, because Z comes straight out of a measured frequency.
Common mistakes and how to avoid them
Changing the characteristic lines with voltage. Voltage changes λ_min and intensity, not the line positions (as long as V is high enough to excite them).
Using Z instead of Z − 1 for Kα. The screening by the remaining K electron matters.
Plotting ν against Z. Moseley's straight line is √ν against Z.
Mixing keV and eV. 30 kV means electrons gain 30,000 eV.
A practice routine
Derive λ_min = hc/(eV) and use it at three voltages.
Estimate Kα energies for four elements and compare each with the data booklet.
Solve two "identify the element" problems from a given line.
Sketch an X-ray spectrum and label the continuous part, the cut-off and the Kα and Kβ lines.
When you know the formulas but lose track of which one a question wants, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer, so you can see whether the question was about the tube or the target.
Start now: estimate the Kα wavelength of molybdenum (Z = 42) and compare it with the booklet's value.
