JEE Main202623 January 2026Morning ShiftChemistryStructure of AtomActual
Which of the following statements regarding the energy of the stationary state is true in the following one - electron systems ?
Options
- A+2.18 10⁻¹⁸ ~J for second orbit of He ⁺ ion
- B-2.18 10⁻¹⁸ ~J for third orbit of Li ²⁺ ion
- C-1.09 10⁻¹⁸ ~J for second orbit of H atom.
- D+8.72 10⁻¹⁸ ~J for first orbit of He ⁺ ion
Correct answer
B. -2.18 10⁻¹⁸ ~J for third orbit of Li ²⁺ ion
Step-by-step solution
The energy of an electron in the n^ th stationary state of a one-electron system is given by the Bohr's 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 option (1): Second orbit of He^+ ( Z=2, n=2 ) E = -2.18 10⁻¹⁸ 2^2 2^2 = -2.18 10⁻¹⁸ J. (Incorrect sign in option) For option (2): Third orbit of Li²⁺ ( Z=3, n=3 ) E = -2.18 10⁻¹⁸ 3^2 3^2 = -2.18 10⁻¹⁸ J. (Correct) For option (3): Second orbit of H atom ( Z=1, n=2 ) E = -2.18 10⁻¹⁸ 1^2 2^2 = -0.545 10⁻¹⁸ J.