GATE CY Structure PYQs & Answers — Page 3

Questions 21–30 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 3 of 5

and

are the normalized eigenfunctions of two hydrogen atoms H

and H

, respectively. If

, the option that is ALWAYS CORRECT is

Your answerChoose one option.

imaginary constant

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For the angular momentum operator

and the spherical harmonics

The value of

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For three operators

, and

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

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The state of the electron in a He

ion is described by the following normalized wavefunction,

. Here,

and

represent the radial and angular components of the eigenfunctions of He

ion, respectively, and

is an unknown constant. If the energy of the ion is measured in the above state, the probability (rounded off to two decimal places) of obtaining the energy of

atom unit is

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A certain wavefunction for the hydrogen-like atom is given by

. The number of node(s) in this wavefunction is

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Acceptable wavefunctions for a quantum particle must be:

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

odd

even

single-valued

continuous

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The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 m s⁻¹ (rounded off to one decimal place) is ________ picometers. [N = 6.022 × 10²³; h = 6.626 × 10⁻³⁴ kg m² s⁻¹]

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Among the following linear combination of atomic orbitals, the CORRECT representation of the lowest unoccupied π-molecular orbital of butadiene is:

Your answerChoose one option.

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Among the following,

the total number of aromatic species is ______

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The hydrogen-like radial wave function of the

orbital is given as

where

;

atomic number;

distance from the nucleus and

Bohr radius.

Positions of the radial nodes (in units of

) of the

orbital are at

Your answerChoose one option.

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GATE CY Structure PYQs

Question 20

Question 35

Question 56

Question 59

Question 60

Question 16

Question 47

Question 13

Question 17

Question 41