JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Atomic Structure

The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state

Ψ

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

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

Answer: (A), (C)

Solution

For

He^{+}

(Z = 2), the energy is given by:

E = \frac{- 13.6 \times Z ^{2}}{n ^{2}} = \frac{- 13.6 \times 4}{n ^{2}} = - 3.4

Solving:

n^{2} = 16

, so

n = 4

.

Given

ℓ = 2

and

m = 0

Angular nodes = $ℓ = 2$ ✓ (option 1 correct)
Radial nodes = $n - ℓ - 1 = 4 - 2 - 1 = 1$ (option 2 incorrect)
The state is 4d ✓ (option 3 correct)
The nuclear charge experienced is the full $Z = 2 e$ (no shielding in one-electron ion), so option 4 is incorrect.

Correct answers: (1) and (3).

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · One or more correct options

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JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Atomic Structure

Solution

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