From a6985853aa57c2d6b765b68e1e2c4415c5ffc45b Mon Sep 17 00:00:00 2001 From: Kostas Vilkelis <kostasvilkelis@gmail.com> Date: Wed, 24 Feb 2021 13:59:21 +0000 Subject: [PATCH] Specify exercise 3 assumptions --- src/1_einstein_model.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/1_einstein_model.md b/src/1_einstein_model.md index 9b177476..e79ddd4f 100644 --- a/src/1_einstein_model.md +++ b/src/1_einstein_model.md @@ -527,7 +527,7 @@ $$ ### Exercise 3: Total heat capacity of a diatomic material -One of the assumptions of the Einstein model states that every atom in a solid oscillates with the same frequency $\omega_0$. However, if the solid contains different types of atoms, it is unreasonable to assume that the atoms oscillate with the same frequency. One example of such a solid is a lithium crystal, 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. +One of the assumptions of the Einstein model states that every atom in a solid oscillates with the same frequency $\omega_0$. However, if the solid contains different types of atoms, it is unreasonable to assume that the atoms oscillate with the same frequency. One example of such a solid is a lithium crystal, 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. Assume that the solid is 1D (1D quantum harmonic oscillator). 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 each atom of the lithium crystal, assuming that all $^6$Li atoms are in $n=2$ vibrational mode and all $^7$Li atoms are in $n=4$ vibrational mode. -- GitLab