GATE CY Structure PYQs & Answers — Page 2

Questions 11–20 of 46. Imported answers require independent review unless marked reviewed.

The kinetic energies of an electron (

) and a proton (

) are

and

, respectively. Given that mass of a proton is 1836 times that of an electron, the ratio of their de Broglie wavelengths (

) is_____ (rounded off to two decimal places).

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The value of

in atomic unit of energy is _____. (

: charge of electron;

: Bohr radius;

: permittivity of vacuum) (rounded off to the nearest integer)

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, and

are four Hückel molecular orbitals of benzene with orbital energies

, and

, respectively.

The correct order of the orbital energies is

(The six carbon atoms of benzene are denoted by A to F and

is the

orbital of

carbon of benzene.)

Your answerChoose one option.

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Among the following, the correct statement(s) is (are):

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

the normalization factor of a Slater determinant for a 3-electron atom is

the number of nodes in the radial wave function of 3s orbital of a hydrogen atom is the same as the number of nodes in the angular wave function of a 4d orbital of hydrogen atom.

the energy separation between any two adjacent states is same for a harmonic oscillator, while it is different for a rigid rotor.

the magnitude of the total spin angular momentum of an

electron is the negative of that of a

electron.

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The wave function of a particle in a cubic box (of side

) is given by

The ratio of the energy of the state corresponding to the above wave function to the ground state energy is ____.

(rounded off to the nearest integer)

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and

are normalized eigenfunctions of a Hermitian operator.

and

The value of

is __.

(rounded off to the nearest integer)

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The INCORRECT statement is

Your answerChoose one option.

Zero-point energy of a quantum mechanical harmonic oscillator of frequency ν is

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

The time independent Schrödinger equation for Li²⁺ can be solved exactly

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

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The wavefunction for Be

in a certain state is given by

, where

is the normalization constant,

is the distance of electron from the nucleus and

is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

Your answerChoose one option.

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Match the following

Column I

(P) Associated Legendre polynomials (Q) Hermite polynomials (R) Associated Laguerre polynomials (S) Trigonometric functions

Column II

(I) Harmonic oscillator (II) Particle in a box model (III) Angular part of H atom (IV) Radial part of H atom

Your answerChoose one option.

P→II, Q→I, R→IV, S→II

P→II, Q→IV, R→II, S→I

P→IV, Q→I, R→III, S→II

P→II, Q→III, R→IV, S→I

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The correct statement(s) for XeF₂ is(are)

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

Its bonding is best explained by classical 2-centered-2-electron bonds

Its bonding is best explained by a non-classical 3-centered-4-electron bond

It contains nine lone pairs of electrons

Its point group is D∞h

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GATE CY Structure PYQs

Question 60

Question 33

Question 44

Question 56

Question 62

Question 63

Question 28

Question 44

Question 45

Question 55