2005. 4.22
Total:60%
1.When the motion of gaseous molecules of mass m is confined in a
two-dimensional plane at temperature T, what is their mean speed? (5%)
How does it compare to the cases of moving in just a given direction and of
traveling in a three-dimensional space? (5%)
2.A beam of He-atom passes through a cell containing CH4 molecules. Let ι be
the cell length and λ be the mean free path of the He-CH4 collision.
(1)Show that the probability of He-atom having exactly two collisions is
ι^2
P2 = ───exp(-ι/λ)
2λ^2 (10%)
(2)After passing through the cell, the flux of He-atom beam is attenuated by
10%, what are the probabilities for those with just one collision and
with no collision? (5%)
3.A student put a mixture of H2, D2, and HD gases in a glass bulb. He only
knows the rotational B constant for H2 is about 60 cm-1, and wishes to
estimate the population ratios of rotational states j=1 and 0 for the three
molecules at 500K. Can you help him on this? (15%)
4.A student synthesized an odor compound and wished to characterize its
electronic excited state lifetime. He put it into a vacuum cell and
employed a laser spectroscopic technique for measurement, obtaining a
lifetime of 3μs. Later, he found out that the cell had a small leak
resulting in a pressure of 1 torr. So, he fixed the leak and pumped down
the cell to 10^-5 torr. Then he repeated the measurement again. This time
he observed 30μs for lifetime! He was puzzled. Can you explain to him
these results? What information can he obtain from these measurements?
(10%)
5.The destruction of stratospheric ozone is an extremely important problem in
environmental chemistry. Back in 1930 Chapman suggested a mechanism for
atmospheric ozone formation and destruction, Which involved several key
elementary reactions,
O2 + hν(λ<240nm) ─k1─→ O + O
O + O2 + M ─k2─→ O3 + M
O3 + hν(240nm<λ<320nm) ─k3─→ O + O2
O + O3 ─k4─→ O2 + O2
Given the currently known values of k1=10^12 s^-1,
k2=2×10^-33 cm^6 molecule^-2 s^-1, k3=3×10^-4 s^-1,
k4=10^-15 cm^3 molecule^-1 s^-1, and the fact that in stratosphere the air
has a lower density of 5×10^17 molecules/cm^3, and with about the same
composition as that in troposphere. Can you estimate the concentrations of
stratospheric ozone and O-atom based on the Chapman mechanism? (10%)
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