Dr. Daniel Spemann WS 2012/13
Nukleare Festk¨rperphysik Sheet 7
Fakult¨t f¨r Physik und Geowissenschaften
Exercises in Nuclear Physics
Task 1: (6 points)
A “hot spot” is a strong radioactive source, possibly of just one certain isotope, with very strong speciﬁc
activity and the size of a dust particle. A punctual “hot spot” of 106 Ru is ﬁxed at a certain point of the
lung and irradiates the tissue there hemispherically. 106 Ru is a 40 keV-β-source with a half-life T1/2 =
367 d. The activity of the “hot spot” is 100 µCi and the penetration depth of the radiation is 0.1 mm
in average. Calculate the number of 106 Ru atoms of the “hot spot” and the energy dose the surrounding
tissue is exposed to (human tissue mainly consists of water).
Task 2: (5 points)
The decay of 57 Co via electron capture to the 57 Fe ground state has two intermediate states (see decay
scheme). What are the multipolarities l and types (E,M) of γ-radiation emitted in the two transitions in
the 57 Fe nucleus? Which of them are the most probable ones?
Task 3: (10 points)
In the Pound-Rebka-experiment the M¨ßbauer-eﬀect was used to determine the wavelength shift of γ-
quanta in the gravitational ﬁeld of the earth.
a) What is the relative frequency shift of a γ-quantum in the gravitational ﬁeld of the earth for a
height diﬀerence of h = 23 m between source and absorber?
b) Compare this result with the natural line width of the 14.4 keV γ-line of the transition in the 57 Fe
(half-life of the excited state T1/2 = 98 ns)!
c) In the experiment a 57 Co source with an activity of 0.4 Ci was used. How many 14.4 keV γ-quanta
can be expected at the absorber per second (distance h = 23 m, diameter d = 7.62 cm), if a scattering
of the quanta between source and absorber can be neglected?