A hydrogen-like species in its ground state absorbs 1.744 10⁻¹⁷ J of energy and its electron gets excited to the second excited state. The atomic number of this species is ________. Given : R_H = 2.18 10⁻¹⁸ J

Step-by-step solution

The energy difference between two energy levels for a hydrogen-like species is given by: E = R_H Z^2 [ 1 n₁^2 - 1 n₂^2 ] The electron transitions from the ground state ( n₁ = 1 ) to the second excited state ( n₂ = 3 ). Substituting the given values into the formula: 1.744 10⁻¹⁷ = 2.18 10⁻¹⁸ Z^2 [ 1 1^2 - 1 3^2 ] 17.44 10⁻¹⁸ = 2.18 10⁻¹⁸ Z^2 [ 1 - 1 9 ] 8 = Z^2 8 9 Z^2 = 9 Z = 3 The atomic number of the species is 3. Answer: 3