How to calculate the emission wavelength of a substance?
There is no general way. 

For a particular case, there is need a good quantum chemistry model of energy levels, and a knowledge of character of the emission. It could be an elastic excitation, releasing the same wavelength. It can be fluorescence or phosphorescence with longer wavelength.

For very simple cases, like a hydrogen atom, it is easy and googleable. See the Rydberg constant :


  $$\frac{1}{\lambda} = Ry \cdot {1\over h} \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=\frac{m_\text{e} e^4}{8 \varepsilon_0^2 h^3} \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$
  where $n_1$  and $n_2$ are any two different positive integers (1, 2, 3, ...), and $\lambda$ is the wavelength (in vacuum) of the emitted or absorbed light.
  
  $$\frac{1}{\lambda} =  R_M\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$
  
  where $R_M = R_\infty/(1+m_{\text{e}}/M)$ and $M$ is the total mass of the nucleus. This formula comes from substituting the  of the electron.


The more complex the real scenario is, the less are usable theoretical models and chemists must rely either on experimental data, either on empirical models not supported by underlying theoretical principle. 

There is an example of mercury melting point. Experimentally, it is a piece of cake, some $\pu{-38.8 ^{\circ}C}$. Theoretically, physical chemists waited more then 50 years until there were recently powerful enough computers available. It took combination of extensive relativistic quantum chemistry computations and random calculations to reach result within $\pu{\pm 1 ^{\circ}C}$ error. The prior non-relativistic calculations predicted the melting point with the error more than $\pu{100 ^{\circ}C}$ !!