A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between - 0 . 85 eV and - 0 . 544 eV (including both these values). Find the atomic number of the atom. (Take hc = 1240 eV nm , ground state energy of hydrogen atom = - 13 . 6 eV )

Step-by-step solution

Total 6 lines are emitted. Therefore, n ( n - 1 ) 2 = 6 or n = 4 So, transition is taking place between m th energy state and (m + 3) th energy state. E m = - 0. 85 eV Or - 13.6 ( z 2 m 2 ) = - 0.85 Or z m = 0. 25 ... (i) Similarly, E m + 3 = - 0. 544 eV or - 13.6 z 2 ( m + 3 ) 2 = - 0. 544 or z ( m + 3 ) = 0.2 … ( i i ) ...(ii) Solving Eqs. (i) and (ii) for z and m, we get m = 12 and z = 3