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The ground state energy of hydrogen atom is $- 13.6 eV$ . 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 is / true for the state $ψ$

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It has 2 angular nodes

It has 3 radial nodes

It is a 4d state

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

answer is A, C.

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Detailed Solution

$\begin{array}{c} - 3.4 = \frac{- 13.6 \times 4}{n^{2}} \\ n = 4 \end{array}$

$\begin{array}{ll} ℓ = 2 \\ m = 0 \end{array}$

Angular nodes $= ℓ = 2$

Radial nodes $= (n - ℓ - 1) = 1$

$n ℓ = 4 d state.$

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