- #1
Diracobama2181
- 70
- 3
- Homework Statement
- Consider the formation of diatomic molecules $$A_2$$ out of atoms $$A$$. Assume that the binding energy of the molecule is $$I$$, i.e., the difference in internal energy between a molecule and a pair of atoms is $$−I$$. Show that in the limit when the atoms and molecules may be regarded as classical ideal gases, except for the formation of the molecules, the equilibrium densities of the atoms and molecules satisfy $$\frac{nA_2}{n_ A^2} = √ 8λ 3 Ae I kT $$.
- Relevant Equations
- $$\mu_{A_2}+\mu_{A}=0$$
It is my assumption that I need to find the chemical potential of the atoms $$\mu_A$$ and for the molecules $$\mu_{A_2}$$,
then use $$\mu_{A_2}+\mu_{A}=0$$ to arrive at the given identity. For $$\mu_A$$, I found that $$\mu_A=k_BTln(n_A\lambda ^3)$$, where
$$n_a=\frac{N_a}{V}$$ and $$\lambda$$ is the thermal wavelength. My question is, how would I go about find $$\mu_{A_2}$$? I know I can find it using the partition function. But I am unsure what that would be in this case. Any advice helps. Thanks
then use $$\mu_{A_2}+\mu_{A}=0$$ to arrive at the given identity. For $$\mu_A$$, I found that $$\mu_A=k_BTln(n_A\lambda ^3)$$, where
$$n_a=\frac{N_a}{V}$$ and $$\lambda$$ is the thermal wavelength. My question is, how would I go about find $$\mu_{A_2}$$? I know I can find it using the partition function. But I am unsure what that would be in this case. Any advice helps. Thanks