All questions are worth the same number of points.
Make sure that you include detailed working. Answers with zero working will garner zero points!
Question 1: Definitions
Give a succinct definition (with a very brief illustrative example,
if applicable) for the following five concepts.
A maximum of five
concise (non-rambling) sentences is allowed for each definition.
A
maximum of five concise sentences is allowed for each example, where
applicable.
Question 2.
Read through the example about haemoglobin on KK pp140-143.
(a) KK5.8 Carbon monoxide poisoning.
(b) In a real haemoglobin molecule, the tendency of oxygen to bind to a haeme site increases as the other three haeme sites become occupied. To model this effect in a simple way, imagine that a haemoglobin molecule has just two sites, either or both of which can be occupied. This system has four possible states (with only oxygen present). Take the energy of the unoccupied state to be zero, the energies of the two singly occupied states to be -0.55eV, and the energy of the doubly occupied state to be -1.3eV (so the change in energy upon binding the second oxygen is -0.75eV). Calculate and plot the fraction of occupied haeme sites as a function of the effective partial pressure of oxygen. Can you think why this behaviour might be preferable for the function of haemoglobin? Can you think why the lowered binding energy for double occupation occurs?
Question 3.
KK5.12 Ascent of sap in trees.
Question 4.
Consider a system of five particles, inside a container where the
allowed energy levels are nondegenerate and evenly spaced. (For
instance, the particles could be trapped in a one-dimensional harmonic
oscillator potential.) In this problem you will consider the allowed
states for this system, depending on whether the particles are
identical fermions, identical bosons, or distinguishable particles.
(a) Describe the ground state of this system, for each of these three
cases.
(b) Suppose that the system has one unit of energy (above the ground
state). Describe the allowed states of the system, for each of the
three cases. How many possible system states are there in each
case?
(c) Repeat part (b) for two units of energy and for three units of
energy.
(d) Suppose that the temperature of this system is low, so that the
total energy is low (though not necessarily zero). In what way will
the behaviour of the bosonic system differ from that of the system of
distinguishable particles? Discuss.
Question 5.
(a) KK6.1 Derivative of Fermi-Dirac function.
(b) Repeat for the Bose-Einstein distribution function.