(1) The atomic numbers of the target materials in two X-ray tubes are in the ratio 1:3. The X-ray photon energies of the Kα lines of these materials are in the ratio
(a) 1:3 (b) 3:1 (c) 1:√3 (d) 1:9 (e) 1:1
According to Mosley’s law, the frequency ‘ν’ of a particular characteristic X-ray (such as Kα) is directly proportional to the square of the atomic number of the target. Since the photon energy is hν, it follows that the energy is directly proportional to the square of the atomic number. Therefore, the energies are in the ratio 1:9.
(2) The minimum wave length of X-rays produced by an X-ray tube operating at an anode voltage of 24.8 kV is very nearly
(a) 1.8 Ǻ (b) 1.5 Ǻ (c) 1 Ǻ (d) 0.8 Ǻ (e) 0.5 Ǻ
The minimum wave length X-ray photon will have the entire energy of the impinging electron, which is 24.8 keV.
Since the product of the photon energy in eV and the wave length in Angstrom is 12400, the minimum wave length is 12400 ÷ 24800 = 05 Ǻ.
[You may use the equation hc/λ = 24800 eV= 24800×1.6×10–19 joule to calculate λ in metre after substituting for Planck’s constant ‘h’ and the speed of light ‘c’, but it will be time consuming].
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