Phys 2053: Homework III
due February 7, 2014
1. Hydrogen Spectra (3 p)
Calculate the wave lengths of the following transitions:
(a) the first member of the Lyman Series
(b) the third member of the Balmer Series
(c) the second member of the Paschen Series
2. Beryllium Spectra (3 p)
Calculate the two longest wave lengths of the Balmer series of triply ionized beryllium
(Z=4), and determine if they are in the visible spectrum.
3. Lithium Spectra (3 p)
Adjacent wavelengths 72.9 nm and 54.0 nm are found in one series of transitions among
the radiations emitted by doubly-ionized lithium. Find the value of n0 for this series and
find the next wavelength in the series.
4. Bragg Scattering I (2 p)
A single crystal of table salt (NaCl) is irradiated with a beam of X-rays of wavelength
0.25 nm, and the first Bragg reflection is observed at an angle of 26.3o .
(a) What is the atomic spacing of the NaCl crystal?
(b) What angle of the incidence will produce the 2nd order Bragg peak?
4. Bragg Scattering II (4 p)
Monochromatic X-rays are incident on a crystal in the geometry of Fig. 1.10 in Morrison.
The first order Bragg peak is observed when the angle of incidence is 34o . The crystal
spacing is known to be 0.347 nm.
(a) What is the wavelength of the X-rays.?
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(b) Consider a set of crystal planes that make an angle of 45o with the surface of the
crystal as indicated in Fig 1. For X-rays of the same wavelength, find the angle
of incidence measured from the surface of the crystal that produces the first order
Bragg peak. At what angle of the surface does the emerging beam appear in this
case?
Figure 1: An incident beam of X-rays can be reflected from many different crystal planes.
5. Compton Scattering (4 p)
X-ray photons of wavelength 0.0248 nm are incident on a target, and the Comptonscattered photons are observed at 90o .
(a) What is the wavelength of the scattered photons?
(b) What is the momentum of the incident photons and of the scattered photons?
(c) What is the kinetic energy of the scattered electrons?
(d) What is the momentum (magnitude and direction] of the scattered electrons?
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