A hydrogen sample is prepared in a particular excited state A of quantum number, n_A=3 . The ground state energy of hydrogen atom is -|E| . The photons of energy |E| 12 are absorbed in the sample which results in the excitation of some electrons to excited state B of quantum number n_B , whose value is

Step-by-step solution

Given, energy of hydrogen atom in ground state =-|E| and n_A=3 Energy of electrons in excited state, n_A (E)_ n_A = -|E| n_A^2 Energy of electrons in excited state, n_B =(E)_ n B = -(E) n_B^2 When sample absorbs the photon of energy, |E| 12 , then its electrons reaches from energy state n_A to energy state n_B . aligned & Hence, (E)_ n_B -(E)_ n_A = |E| 12 & -|E| n_B^2 - -|E| n_A^2 = |E| 12 & -1 n_B^2 + 1 n_A^2 = 1 12 - 1 n_B^2 = 1 12 - 1 n_A^2 & = 1 12 - 1 9 - 1 n_B^2 =- 1 36 & n_B^2=36 & n_B=6 & aligned