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src/solutions/1_einstein_model.md

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 # Solutions for lecture 1 exercises
 
 ### Exercise 1: Heat capacity of a classical oscillator.
@@ -84,12 +74,12 @@ Use the formula $\omega = \sqrt{\frac{k}{m}}$.
 
 2.
 
-$E = \frac{N_{^6Li}}{N}\hbar\omega_{^6Li}(2 + 1/2)+\frac{N_{^7Li}}{N}\hbar\omega_{^7Li}(4 + 1/2)$.
+$E = N_{^6Li}\hbar\omega_{^6Li}(2 + 1/2)+N_{^7Li}\hbar\omega_{^7Li}(4 + 1/2)$.
 
 3.
 
-$E = \hbar\omega_{^6Li}\left(n_B(\beta\hbar\omega_{^6Li}) + \frac{1}{2}\right) + \hbar\omega_{^7Li}\left(n_B(\beta\hbar\omega_{^7Li}) + \frac{1}{2}\right)$.
+$E = N_{^6Li}\hbar\omega_{^6Li}\left(n_B(\beta\hbar\omega_{^6Li}) + \frac{1}{2}\right) + N_{^7Li}\hbar\omega_{^7Li}\left(n_B(\beta\hbar\omega_{^7Li}) + \frac{1}{2}\right)$.
 
 4.
 
-$C = C_{^6Li} + C_{^7Li}$ where the heat capacities are calculated with the formula from Excercise 2.4.
+$C = \frac{N_{^6Li}}{N}C_{^6Li} + \frac{N_{^7Li}}{N}C_{^7Li}$ where the heat capacities are calculated with the formula from Excercise 2.4.