So I was wondering that atomic spectrum for each element is different.This implies that wavelength of electron which is given by $\lambda= \frac{nh}{2\pi}$ (according to Bohr's theory).
Also $n$ represents the number of orbit which happens to be equal to number of wavelengths of a stationary wave, since you cannot have anything between two integral numbers for $n$.
How does it work for other atoms if it does not then what else does?
Bohr's theory works only for 1 electron systems. i.e, H atom He{+} ion, Li{+2} ion etc. Once you have an extra electron, say He atom, then the exact solution of Schrodinger equation is not possible and one has to resort to approximation techniques. As a first starting point, one resorts to Hartree-Fock(HF) method, which is a variational one. For better accuracy, to match with the experimental results, more sophisticated approximations are used. If you are keen to understand more about this, refer to any good book on quantum chemistry. For example, the book by Szabo & Ostlund or the one by Levine are good. Hope this helps.
