Hydrogen and Hydrogen-like Atoms - Physical Chemistry - Chemistry Previous Year Questions

1

2008 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2008

The ground state electronic energy (Hartree) of a helium atom, neglecting the inter-electron repulsion, is

A

-1.0

B

-0.5

C

-2.0

D

-4.0

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2

2012 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2012

The angular part of the wavefunction for the electron in a hydrogen atom is proportional to \( \sin^2 \theta \cos \theta e^{2i\phi} \). The values of the azimuthal quantum number (\( l \)) and the magnetic quantum number (\( m \)) are, respectively

A

2 and 2

B

2 and -2

C

3 and 2

D

3 and -2

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3

2014 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2014

The overall yield (in %) for the following reaction sequence is__________________

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4

2014 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2014

ψ = N r (6 − Z r) e^−Zr/3 cos θ , is a proposed hydrogenic wavefunction, where Z = Atomic number, r = radial distance from the nucleus, θ = azimuthal angle, N is a constant. The INCORRECT statement about ψ is

A

ψ = 0 in the xy-plane

B

two radial nodes are present in ψ

C

one angular node is present in ψ

D

the size of the orbital decreases with increase in atomic number

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5

2016 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2016

The experimental ionization energies of hydrogen and helium atoms in their ground states are, respectively, 13.6 eV and 24.6 eV. The ground state energy of helium atom, in eV, is

A

-1/2(13.6) - 24.6

B

-4(13.6) - 24.6

C

-1/4(13.6) - 24.6

D

-2(13.6) - 24.6

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6

2023 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2023

The INCORRECT statement is

A

Zero-point energy of a quantum mechanical harmonic oscillator of frequency \(\nu\) is \(\frac{h\nu}{2}\)

B

Energy level of a quantum mechanical rigid rotor is inversely proportional to its moment of inertia

C

The time independent Schrödinger equation for Li²⁺ cannot be solved exactly

D

Total angular momentum of an atomic system is equal to the sum of orbital angular momentum and spin angular momentum

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7

2023 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2023

The wavefunction for Be³⁺ in a certain state is given by \(\psi = N e^{-\left(\frac{4}{a_0}\right) r}\), where \(N\) is the normalization constant, \(r\) is the distance of electron from the nucleus and \(a_0\) is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

A

\(4a_0\)

B

\(\frac{a_0}{4}\)

C

\(8a_0\)

D

\(\frac{a_0}{8}\)

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8

2024 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2024

The value of \(\frac{e^2}{2\pi\epsilon_0 a_0}\) in atomic unit of energy is ____.
(\(e\): charge of electron; \(a_0\): Bohr radius; \(\epsilon_0\): permittivity of vacuum)
(rounded off to the nearest integer)

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9

2007 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2007

The ionisation potential of hydrogen atom is 13.6 eV. The first ionisation potential of a sodium atom, assuming that the energy of its outer electron can be represented by a H-atom like model with an effective nuclear charge of 1.84, is

A

46.0 eV

B

11.5 eV

C

5.1 eV

D

2.9 eV

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10

2017 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2017

The angle of orientation (in degrees) of the angular momentum vector with respect to z-axis for l = 2 and m_l = +2 state of H-atom is ________________________ (up to two decimal places)

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11

2020 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2020

The hydrogen-like radial wave function of the 3s orbital is given as
\[ R_{3,0} = \frac{1}{9\sqrt{3}} \left(\frac{Z}{a_0}\right)^{3/2} \left(6 - 2\rho + \frac{\rho^2}{9}\right) e^{-\rho/6} \]
where \( \rho = 2Zr/a_0 \); \( Z \) = atomic number; \( r \) = distance from the nucleus and \( a_0 \) = Bohr radius.
Positions of the radial nodes (in units of \( a_0 \)) of the 3s orbital are at

A

\(\frac{3 + \sqrt{3}}{2Z}, \frac{3 - \sqrt{3}}{2Z} \)

B

\(\frac{6 + 3\sqrt{3}}{2Z}, \frac{6 - 3\sqrt{3}}{2Z} \)

C

\(\frac{3 + \sqrt{3}}{Z}, \frac{3 - \sqrt{3}}{Z} \)

D

\(\mathbf{T} > \mathbf{Q} > \mathbf{R} > \mathbf{P} > \mathbf{S} \)

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12

2022 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2022

A certain wavefunction for the hydrogen-like atom is given by
\[ \Psi(r, \theta, \phi) = \frac{2^{\frac{1}{2}}}{81\pi^{\frac{1}{2}}} \left(\frac{Z}{a_0}\right)^{5/2} \left(6 - \frac{Zr}{a_0}\right) r e^{-Zr/3a_0} \cos\theta. \]
The number of node(s) in this wavefunction is

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13

2026 · Chemistry · Physical Chemistry · Hydrogen and Hydrogen-like Atoms

Chemistry (CY) 2026

The orbital angular momentum (L) of an electron is √12ħ. The minimum angle between L and its z-component (in degrees) is ______ (rounded off to one decimal place).

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