Download Department of Physics, UCC PY 1054: Astronomy: Problem Set 7 In

Department of Physics, UCC
PY 1054: Astronomy: Problem Set 7
In the first part of this exercise we continue our investigation of some of the basic
properties of the Universe.
(a) The age of our Galaxy can be estimated by the radioactive decay of Uranium. Uranium
is produced in Supernovae explosions, which result in the generation of two isotopes
U235 and U236 , with an initial relative abundance ratio of 1.65 (i.e. number of U235
atoms divided by the number of U236 atoms). The decay constants (λ) of these isotopes
are 0.97×10−9 yr−1 and 0.15×10−9 yr−1 respectively. If the current abundance ratio
is 0.0072, estimate the age of our Galaxy.
(b) The present number of electrons in the Universe is the same as that of protons
∼0.2 m−3 . Consider a time in the early history of the Universe with it was 1 millionth
of its present size (in linear units). What was the number density of electrons (ne
m−3 ) then ?
(c) Given that the mean free path of photons through an electron gas λ ∼ 1/ne σ, where
σ = 6.7×10−29 m−2 , calculate λ.
(d) What was the typical time between interactions ? Compare this interaction time with
the age of the Universe at that time, ∼10,000 years. What does this tell you about
the degree to which photons interacted with electrons ?
Some numbers you might need:
Gravitational constant (G) = 6.67×10−11 N m2 kg−2
Speed of light (c) = 3×108 m s−1
Stefan constant (σ) = 5.67×10−8 W m−2 K−4
Solar mass (M ) = 2 × 1030 kg
Solar radius (R ) = 7 × 108 m
Solar Luminosity = 3.85 × 1026 W
1 pc = 3.086 × 1016 m
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