COMEDK2023Evening ShiftChemistryStructure of AtomActual
The energy of an electron in the ground state of Hydrogen atom is -2.18 10⁻¹⁸ ~J . What would be the energy associated with the second excited state of Li ?
Options
- A-0.242 10⁻¹⁸ ~J
- B-4.905 10⁻¹⁸ ~J
- C-2.18 10⁻¹⁸ ~J
- D-3.26 10⁻¹⁸ ~J
Correct answer
C. -2.18 10⁻¹⁸ ~J
Step-by-step solution
The energy of an electron in a hydrogen-like species is given by the formula E_n = -2.18 10⁻¹⁸ Z^2 n^2 J , where Z is the atomic number and n is the principal quantum number. For Lithium (Li), the atomic number Z = 3 . The ground state corresponds to n = 1 , the first excited state to n = 2 , and the second excited state to n = 3 . Substituting Z = 3 and n = 3 into the formula: E₃ = -2.18 10⁻¹⁸ 3^2 3^2 J E₃ = -2.18 10⁻¹⁸ 9 9 J E₃ = -2.18 10⁻¹⁸ J Answer: -2.18 10⁻¹⁸ ~J