A hydrogen atom changes its state from \( n = 3 \) to \( n = 2 \). Due to recoil, the percentage change in the wavelength of emitted light is approximately \( 1 \times 10^{-n} \). The value of \( n \) is ______. \([ \text{Given: } Rhc = 13.6 \, \text{eV}, \, hc = 1242 \, \text{eV nm}, \, h = 6.6 \times 10^{-34} \, \text{J s}, \, \text{mass of the hydrogen atom} = 1.6 \times 10^{-27} \, \text{kg} ]\)