GATE PH concept:hydrogen-atom PYQs & Answers

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concept:hydrogen-atom

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Questions 1–8 of 8. Imported answers require independent review unless marked reviewed.

Topic practice 8 questionsPage 1 of 1

Consider an electron in the energy eigenstate

of the hydrogen atom. Given that the radial probability distribution of the electron in such a state takes its maximum value at

, where

is the Bohr radius, and

is an integer. The value of

(in integer) is ____

The radial part of the wavefunction

is given by

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Which of the following option(s) is/are correct for the ground state of a hydrogen atom?

Your answerSelect all correct options. You can choose more than one.

Linear Stark effect is zero

It has definite parity

Spin-orbit coupling is zero

Hyperfine splitting is zero

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is the Hamiltonian,

the orbital angular momentum and

is the z-component of

. The

state of the hydrogen atom in the non-relativistic formalism is an eigen function of which one of the following sets of operators?

Your answerChoose one option.

and

only

and

only

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The normalized radial wave function of the second excited state of hydrogen atom is

where

is the Bohr radius and

is the distance from the center of the atom. The distance at which the electron is most likely to be found is

. The value of

(in integer) is _____.

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An electric field

is applied to a Hydrogen atom in

excited state. Ignoring spin, the

state is fourfold degenerate, which in the

basis are given by

and

. If

is the interaction Hamiltonian corresponding to the applied electric field, which of the following matrix elements is nonzero?

Your answerChoose one option.

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The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (

is the Bohr radius)

Your answerChoose one option.

zero

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The electronic ground state energy of the Hydrogen atom is

eV. The highest possible electronic energy eigenstate has an energy equal to

Your answerChoose one option.

1 eV

+13.6 eV

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Positronium is an atom made of an electron and a positron. Given the Bohr radius for the ground state of the Hydrogen atom to be 0.53 Angstroms, the Bohr radius for the ground state of positronium is ________ Angstroms. (up to two decimal places).

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GATE PH concept:hydrogen-atom PYQs

How to practice concept:hydrogen-atom

Question 29

Question 24

Question 15

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Question 6

Question 15

Question 23

Question 55