Question

Among the following, the correct statement(s) is (are) :

• A. the normalization factor of a Slater determinant for a 3-electron atom is $\sqrt{\frac{1}{3}}$.
• B. the number of nodes in the radial wave function of 3s orbital of a hydrogen atom is the same as the number of nodes in the angular wave function of a 4d orbital of hydrogen atom.
• C. the energy separation between any two adjacent states is same for a harmonic oscillator, while it is different for a rigid rotor.
• D. the magnitude of the total spin angular momentum of an α electron is the negative of that of a ẞ electron.

Answer 1

Answer: (B), (C)

the number of nodes in the radial wave function of 3s orbital of a hydrogen atom is the same as the number of nodes in the angular wave function of a 4d orbital of hydrogen atom.

Answer 2

The correct option is (B) : the number of nodes in the radial wave function of 3s orbital of a hydrogen atom is the same as the number of nodes in the angular wave function of a 4d orbital of hydrogen atom and (C) : the energy separation between any two adjacent states is same for a harmonic oscillator, while it is different for a rigid rotor.