The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation, $E_n=(n+\frac{1}{2})h\nu$ , where n is a quantum number with possible values of 1 , 2 ...... and $\nu$  is the frequency of vibration. The vibration frequency of HCl is approximately $9\times {10}^{11}{s}^{-1}$ . If the minimum energy is required to excite a vibration in HCl is  $\Delta E$ , the wavelength of light required to excite this vibration is______  $\mu m$.
[Given $h=6.6\times {10}^{-34}Js\&c=3\times {10}^{8}m{s}^{-1}$ , Molar mass of HCl = 36.5 g/mol]