15.2 The Boltzmann Factor Flashcards
What’s the probability of rolling one twice on a dice?
The probability of rolling 1 on a dice twice is (1/6)^2 = (1/36)
How is the probability particles will gain a certain multiple of energy defined?
Many particles can acquire or lose energy from random interactions with other particles. This could be energy quanta in a hot solid or electrons in a semi conductor. To go up energy levels, particles must gain quantum E of energy and other particles must lose it for same average energy. If a fraction of f particles acquire this energy, the probability is f.
’ At room temperature the fraction of particles which can gain 0.3eV is f=1.0*10^-5. Calculate the number of particles in one mol that have gained 0.9 eV by chance.’
3 energy gains are made.
Multiply the probability to the power of three, and then multiply by the number of particles in a mol.
6*10^8
What does the fact that particles drop by equal ratios for constant Energy increase show?
The fact that numbers of particles drop by equal ratios for constant increase in energy E shows an exponential relationship.
What is the relationship for number of particles which gain a particular amount of energy?
N=N0e^-E/kt
N= number of particles, N0 is original, and e^-E/kT is the Boltzmann factor, or probability, of particles gaining this energy.
What does the graph log f against E show? what’s the shape of the line?
Log f against E gives a straight line.
For lines plotted, log f falls as energy rises as the probability falls with energy required rising. Liquid nitrogen has weaker intermolecular forces than ionic and covalent bonds and so its probability falls faster with energy rise. Only 300K is needed to break bonds compared to 1500K for ionic and covalent bonds which require more energy at the same temperature.
F against T with a logarithmic curve shows what shape for graphs? On the left end what are features of the graph, how about the right?
A curve which becomes less steep towards the right end.
Cold at left, T is low and E/kT is large. F tends to zero. As temperature increases to the right, it’s higher and E/kT is smaller, so probability tends to one. The graphs start to climb in order van der baals, (weak), hydrogen, then covalent which is strongest so requires a higher temperature.
Explain activation processes.
Activation processes rely on energy acquired by thermal agitation from the background. Liquids flow when molecules in the middle gain enough energy to break out from cage of neighbouring particles. Liquids evaportate when molecules at the surface gain energy to break away from molecules. As a liquid warms, viscosity drops and rate of evaporation rises. F describes temperature dependence. Ionisation of atoms in semi conductor crystals also describes how the number of atoms with energy to liberate one electron varies with T.
