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14 Matter: very hot and very cold



Revision Guide for Chapter 14
Contents
Student's Checklist

Revision Notes
Boltzmann factor........................................................................................................................ 4
Thermal activation processes.................................................................................................... 4
Values of the energy kT ............................................................................................................. 6

Summary Diagrams (OHTs)
Climbing a ladder by chance ..................................................................................................... 7
Temperature and average energy per particle .......................................................................... 8
Average…

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14 Matter: very hot and very cold



Student's Checklist
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I can show my understanding of effects, ideas and
relationships by describing and explaining cases involving:
the ratio of the numbers of particles in a body that exist in states at different energy, and the
change…

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14 Matter: very hot and very cold


the Boltzmann factor exp(­ / kT)

Revision Notes: Boltzmann factor; Activation processes
Summary Diagrams: Variation of Boltzmann factor with temperature; Examples of activation
processes




Advancing Physics A2 3

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14 Matter: very hot and very cold




Revision Notes
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Boltzmann factor
For a large number of particles in thermal equilibrium at temperature T, the ratio of numbers
of particles occupying distinct states which differ by energy is given by the Boltzmann factor
e­ /kT ,…

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14 Matter: very hot and very cold

Activation




energy gap




particles


The Boltzmann factor e ­ / kT is an approximation to the fraction of particles in a large system
at temperature T having a larger than average energy of at least . If the temperature is
increased, the number…

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14 Matter: very hot and very cold


proportional to the Boltzmann factor e­ / kT, where is the energy needed to free an electron.
Hence the conductivity of an intrinsic semiconductor is approximately proportional to e­ / kT:
= 0 e - / kT .

Conductance variation with temperature
for…

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14 Matter: very hot and very cold




Summary Diagrams (OHTs)
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Climbing a ladder by chance

Climbing a ladder of energy by chance


One particle may acquire energy several times With many particles, a fraction f acquire energy
in succession at each step of ladder

fraction…

Page 8

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14 Matter: very hot and very cold



Temperature and average energy per particle

Temperature and energy = kT

temperature energy = kT photons hf = kT
1 MeV 100 GJ mol­1
supernova 6 billion K nuclear binding gamma rays
energy
= 1.0 pm

100 keV 10 GJ mol­1



hard x-rays…

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14 Matter: very hot and very cold


Average energy per particle for various processes

Processes and energy ~
~ kT per particle


1000 100 000
x-ray
photons
inner electrons in atoms liberated emitted
plasmas
form 10000
100
ultraviolet
photons
emitted
outer electrons in atoms liberated ceramics
10 1000
evaporate
ionic…

Page 10

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14 Matter: very hot and very cold


Variation of Boltzmann factor with temperature

Boltzmann factor: the minority with energy /kT



Boltzmann 1 + e­1 exp(­/kT)
factor as a
power of ten +
10­4 + e­10
logarithmic
scale +
10­8 where the action is: e­20
+

+
10­12 /kT from 15…

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