From the nuclear Schrdinger equation of a diatomic molecule with the vibration rotation interaction term involved in, under the Morse potential approximation, we derived the wavefunction relevant not only with vibrational quantum number, but also with rotational one. The Franck Condon factors of the α band system A 2Π→X 2Σ + and the γ band system C 2Π→X 2Σ + of BS molecule are calculated by using the derived wavefunction. In the calculation, the rotational quantum number J takes values from J=0 up to J=200. The results fit for low or high temperature condition and also the condition of strong shock wave.