Physics 410
Spring 2010
HW 18
HW Due 7 April 2010
1.
2.
3.
4.
A “pluton” (I made that up) is a (made-up) particle that (according to my made-up quantum theory) can only have a total energy
that is an integer multiple of 1eV when placed into a special box. In other words, the allowed energies of the pluton are 1 eV, 2
eV, 3 eV, … Inside this special box I have put 10 distinguishable plutons. They do not interact with each other, so that each
individual pluton can have a total energy of n eV, where n > 0. The total energy of these 10 plutons is 20 eV.
a. What is the probability that you will find five of these plutons in the ground state (five of them with an energy of 1eV
each)?
b. Repeat this problem for when the plutons are indistinguishable
A “charon” (I made that up, too) is a particle that, like the pluton, has allowed energies of m eV, where m is an integer greater
than zero. However, unlike the pluton, these energy states are degenerate. There is only one 1 eV, state, but there are two 2 eV
states, three 3 eV states, etc. Consider 4 distinguishable charons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV?
A “hydron” is exactly like a charon in that the number of states per energy is the same. However, hydrons are indistinguishable.
Consider 4 indistinguishable hydrons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV?
A “nixon” is just like a hydron in that it has the same number of states per energy and they are indistinguishable. However, you
can only put two nixons in each allowed state. Consider 4 indistinguishable nixons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV? (Trick question???)
Physics 410
Spring 2010
HW 18
HW Due 7 April 2010
1. A “pluton” (I made that up) is a (made-up) particle that (according to my made-up quantum theory) can only have a total energy
that is an integer multiple of 1eV when placed into a special box. In other words, the allowed energies of the pluton are 1 eV, 2
eV, 3 eV, … Inside this special box I have put 10 distinguishable plutons. They do not interact with each other, so that each
individual pluton can have a total energy of n eV, where n > 0. The total energy of these 10 plutons is 20 eV.
a. What is the probability that you will find five of these plutons in the ground state (five of them with an energy of 1eV
each)?
b. Repeat this problem for when the plutons are indistinguishable
2. A “charon” (I made that up, too) is a particle that, like the pluton, has allowed energies of m eV, where m is an integer greater
than zero. However, unlike the pluton, these energy states are degenerate. There is only one 1 eV, state, but there are two 2 eV
states, three 3 eV states, etc. Consider 4 distinguishable charons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV?
3. A “hydron” is exactly like a charon in that the number of states per energy is the same. However, hydrons are indistinguishable.
Consider 4 indistinguishable hydrons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV?
4. A “nixon” is just like a hydron in that it has the same number of states per energy and they are indistinguishable. However, you
can only put two nixons in each allowed state. Consider 4 indistinguishable nixons with a total energy of 6 eV.
a. How many microstates are there?
b. What is the most probable number of particles with energy = 1 eV? (Trick question???)