JEE Advanced · Chemistry · 2. Atomic Structure

The ground state energy of hydrogen atom is $- 13.6 e V$ . Consider an electronic state $Ψ$ of ${H e}^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are $- 3.4 e V, 2$ and $0$ respectively. Which of the following statement(s) is(are) true for the state $Ψ$ ?

A It has $2$ angular nodes
B It has $3$ radial nodes
C It is a $4 d$ state
D The nuclear charge experienced by the electron in this state is less than $2 e$ , where e is the magnitude of the electronic charge.

Verified Solution

Answer & Solution

Correct Answer

(C) It is a $4 d$ state

Step-by-step Solution

Detailed explanation

∵ E_{H e^{+}} = \frac{- 13.6 (z^{2})}{n^{2}} = \frac{- 13.6 {(2)}^{2}}{n^{2}} = - 3.4

n^{2} = 16

∴ n = 4

n = 4, l = 2, m = 0

belongs to

4 d_{y z}

orbital

\to

Radial nodes

\Rightarrow n - l - 1

\to

Angular nodes

\Rightarrow 4 - 2 - 1 = 1

\to

Angular nodes

\Rightarrow l \Rightarrow 2

Since

H e^{+}

is a single

e^{-}

ion, its nuclear charge experienced.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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 statement(s) is(are) true for the state Ψ ?

Step-by-step Solution

The ground state energy of hydrogen atom is $- 13.6 e V$ . Consider an electronic state $Ψ$ of ${H e}^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are $- 3.4 e V, 2$ and $0$ respectively. Which of the following statement(s) is(are) true for the state $Ψ$ ?