Energy liberated in the de–excitation of hydrogen atom from $3^{rd}$ level to $1^{st}$ level falls on a photo–cathode. Later when the same photo–cathode is exposed to a spectrum of some unknown hydrogen like gas, excited to 2nd energy level, it is found that the 
de–Broglie wavelength of the fastest photoelectrons, now ejected has decreased by a factor of 3. For this new gas, difference of energies of  $2^{nd}$ Lyman line and $1^{st}$ Balmer line found to be 3 times the ionization energy of the hydrogen atom. Select the correct statement(s):