diff --git a/src/1_einstein_model.md b/src/1_einstein_model.md index de0d8f47eea448eed96110bef0099358d68b6ef0..6e57a127962565d186799278afed9ca7fbbbc9dd 100644 --- a/src/1_einstein_model.md +++ b/src/1_einstein_model.md @@ -388,12 +388,12 @@ \$\$ ### Exercise 3: Total heat capacity of a diatomic material -Naturally occurring lithium has [two stable isotopes](https://en.wikipedia.org/wiki/Isotopes_of_lithium): \$^6\$Li (7.5%) and \$^7\$Li (92.5%). Let us extend the Einstein model to take into account the different masses of different isotopes. +We consider a crystal of lithium, which consists of the [two stable isotopes](https://en.wikipedia.org/wiki/Isotopes_of_lithium) \$^6\$Li (7.5%) and \$^7\$Li (92.5%) in their natural abundance. Let us extend the Einstein model to take into account the different masses of these different isotopes. -1. Assume that the strength of the returning force \$k\$ experienced by each atom is the same. What is the difference in the oscillation frequencies of different isotopes of lithium in the lithium crystal? -2. Write down the total energy of lithium assuming that all \$^6\$Li atoms are in \$n=2\$ vibrational state, and all \$^7\$Li atoms are in \$n=4\$ vibrational state. -3. Write down the total energy of lithium at a temperature \$T\$ by modifying the Einstein model. -4. Compute the heat capacity of lithium as a function of \$T\$. +1. Assume that the strength of the returning force \$k\$ experienced by each atom is the same. What is the difference in the oscillation frequencies of the two different isotopes in the lithium crystal? +2. Write down the total energy stored in the vibrations of the atoms of the lithium crystal, assuming that all \$^6\$Li atoms are in \$n=2\$ vibrational state and all \$^7\$Li atoms are in \$n=4\$ vibrational state. +3. Write down the total energy stored in the vibrations of the atoms in the lithium crystal at a temperature \$T\$ by modifying the Einstein model. +4. Compute the heat capacity of the lithium crystal as a function of \$T\$. [^1]: Data source: [Wikipedia](https://en.wikipedia.org/wiki/Heat_capacities_of_the_elements_(data_page)), mainly the CRC Handbook of Chemistry and Physics.