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Question:

The ground state energy of hydrogen atom is -13.6eV. Consider an electronic state Ψ of He⁺ whose energy, azimuthal quantum number and magnetic quantum number are -3.4 eV, 2, and 0, respectively. Which of the following statements(s) is (are) true for the state Ψ?

It is 4d state

It has 3 radial nodes

The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge.

It has 2 angular nodes

Solution:

Correct option is D. It has 2 angular nodes. EHe+ = −13.6 × (2)²/n² = -3.4 = -13.6/4
n² = 16
so n = 4
quantum numbers are n=4, l=2, m=0
so subshell is = d
angular node = l = 2
Radial node = [n - l - 1] = 4 - 2 - 1 = 1