2.2 Problems 95
2.21 A spectral line of atomic hydrogen has its wave number equal to the difference
between the two lines of Balmer series, 486.1 nm and 410.2 nm. To which
series does the spectral line belong?
2.2.3 X-rays
2.22 (a) TheL→Ktransition of an X-ray tube containing a molybdenum (Z=42)
target occurs at a wavelength of 0.0724 nm. Use this information to estimate
the screening parameter of theK-shell electrons in molybdenum.
[Osmania University]
2.23 Calculate the wavelength of theMo(Z=42)KαX-ray line given that the
ionization energy of hydrogen is 13.6 eV
[Adapted from the University of London, Royal Holloway 2002]
2.24 In a block of Cobalt/iron alloy, it is suspected that the Cobalt (Z=27) is
very poorly mixed with the iron (Z=26). Given that the ionization energy
of hydrogen is 13.6 eV predict the energies of theKabsorption edges of the
constituents of the alloy.
[University of London, Royal Holloway 2002]
2.25 Calculate the minimum wavelength of the radiation emitted by an X-ray tube
operated at 30 kV.
[Adapted from the University of London, Royal Holloway 2005]
2.26 If the minimum wavelength from an 80 kV X-ray tube is 0. 15 × 10 −^10 m,
deduce a value for Planck’s constant.
[Adapted from the University of New Castle upon Tyne 1964]
2.27 If the minimum wavelength recorded in the continuous X-ray spectrum from
a 50 kV tube is 0.247A, calculate the value of Plank’s constant. ̊
[Adapted from the University of Durham 1963]
2.28 The wavelength of theKαlineiniron(Z=26) is known to be 193 pm. Then
what would be the wavelength of theKαline in copper (Z=29)?
2.29 An X-ray tube has nickel as target. If the wavelength difference between the
Kαline and the short wave cut-off wavelength of the continuous X-ray spec-
trum is equal to 84 pm, what is the voltage applied to the tube?
2.30 Consider the transitions in heavy atoms which give rise toLαline in X-ray
spectra. How many allowed transitions are possible under the selection rule
Δl=± 1 ,Δj= 0 ,±1.
2.31 When the voltage applied to an X-ray tube increases from 10 to 20 kV the
wavelength difference between theKαline and the short wave cut-off of the
continous X-ray spectrum increases by a factor of 3.0. Identify the target mate-
rial.
2.32 How many elements have theKαlines between 241 and 180 pm?