Quantum Chemistry - 2


20 Questions MCQ Test GATE Chemistry Mock Test Series | Quantum Chemistry - 2


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This mock test of Quantum Chemistry - 2 for Chemistry helps you for every Chemistry entrance exam. This contains 20 Multiple Choice Questions for Chemistry Quantum Chemistry - 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this Quantum Chemistry - 2 quiz give you a good mix of easy questions and tough questions. Chemistry students definitely take this Quantum Chemistry - 2 exercise for a better result in the exam. You can find other Quantum Chemistry - 2 extra questions, long questions & short questions for Chemistry on EduRev as well by searching above.
QUESTION: 1

For the energy level  the probability density for a particle of mass m is a one dimensional potential box of width L is given by

Solution:

Given energy level E = 

So, the given energy level corresponds to n = 3
No, of nodes in ψ= 3 - 1 = 2

Probabilty density 

QUESTION: 2

π-boncl length between C-C atoms. f.i and v is calculated by using the empirical formula,
Rμv = 1.52Å - 0.186 Å Pμv
where Pμv= is π - bond order between μ and v C -atom .
According to HM O theory. delocalization energy o f Benzene is 2|β|. Then T-bond length in Benzene is

Solution:

Since, delocalization energy = 2|β|
So, one extra delocalizedT-bond Benzene.
The total energy of π-bond = 4(According to HMO Theory)
Since, there are 6(C- C ) bond in benzene.
So. each (C-C) bond has 4/6 π-bond = 2/s = 0.66
Now. by using formula,
Rμv = 1.52Å - 0.186 Å x 0.66 = 1.39 Å

QUESTION: 3

According to Huckel molecular orbital theory, the total energy of hypothetical localized Benzene (C6H6) molecule is

Solution:


So, there are three localized tt-bond. Ech have energy = 2α+ 2β
So, total localized energy= 3(2α + 2β) = 6α +6β

*Answer can only contain numeric values
QUESTION: 4

A perturbation  is introduced in a box of width 1 unit, where V0 is ( << 1 ) is a positive constant. The first order energy correction to the first exited state is α V0 . The value of α is_________


Solution:

First excited state wavefimction

First order eneigy correction to the first excited state is

QUESTION: 5

σx , σy and σz  are the Pauli m atrices. The expression is equal to 2σσ+ σσx is equal to 

Solution:

σ+ σσ
= σσy + x σy + σσ
= σσy, as σσ+ σσx = 0
= iσz

QUESTION: 6

For linear momentum vector operator  -and position vector operator   the operator  is equivalent to

Solution:


*Answer can only contain numeric values
QUESTION: 7

The degeneracy of the n = 2 level for a three dimensional isotropic oscillator is ________. (an integer)


Solution:

Degeneracy for a three dimensional isotropic oscillator gn = 
n= 2

QUESTION: 8

The operation of the commutator  on a function f ( x ) is equal to

Solution:

*Answer can only contain numeric values
QUESTION: 9

The degeneracy of a quantum particle in a cubic box having energy three times that of the lowest energy is ________


Solution:

Energy eigenvalue of a particle in a cubic box.

Groimd state energy corresponds to nx = ny = nz = 1

Three times the ground state energy = 

*Answer can only contain numeric values
QUESTION: 10

Consider a normalized molecular orbital  constructed from two different atomic orbitals  and  that fonn an orthonormal set. Here i = √-1. The value of |c|2 is ______ (upto one decim al place)


Solution:

Given: 
Nonnalization condition:

*Answer can only contain numeric values
QUESTION: 11

The normalized wavefiinctions ψ1 and ψ2 correspond to the ground state and the first excited states of a particle in a potential. The operator A acts on the wavefiinctions as The expectation value of the operator A for the state is ________. (upto two decimal places)


Solution:


QUESTION: 12

Three identical non- interacting particles, each of spin 1/2 and mass m. are moving in a one-dimensional infinite potential well given by

the energy of the lowest energy state of the system is:

Solution:

Figure shows the configuration of the lowest energy state of the system

QUESTION: 13

A certain 2-level system lias stationary state energy  with normalized wave functions
 respectively. A small perturbation V is applied on the system such that V12 = 2. The wavefunction of the particle in groimd state collected upto first order, will be

Solution:

Fii'st order collection in the ground state wave function,

Collected ground state wave function,

*Answer can only contain numeric values
QUESTION: 14

Given that work function of a metal is 5 eV and that photons of 9 eV are incident on it. the maximum velocity of emitted electrons is approximately______ x106 m/s (upto one decimal place)


Solution:

Maximum kinetic energy o qf the electrons,

QUESTION: 15

For a system of two spin -1/2 particles, the value 0f 

Solution:

QUESTION: 16

The ground state wave function of hydrogen atom is given by where a0 is the Bohr
radius. The plot of the radial probability density P(r) for the hydrogen atom in the ground state is

Solution:

The radial probability density is given by

Only option (d) satisfies this condition.
 

*Answer can only contain numeric values
QUESTION: 17

A particle of mass m is constrained to move in a circular ring of radius R . When a perturbation

(where a is a real constant) is added, the first order collection to the ground state energy is The value
of η is ______ (up to one decimal place)


Solution:

Wavefiinction for a particle in a circular ring of radius R is given by

Ground state wave function corresponds to m = 0, 
First order collection to ground state energy


 

QUESTION: 18

The wavefiuiction for a linear harmonic oscillator described by N where α and N are constants, has

Solution:



For small values of 
For large values of 
The wavefunction will cut y-axis aty = -2.
ψ is even function. so it is symetric about y-axis.
From the graph, there are two maxima and one minimum only.

*Answer can only contain numeric values
QUESTION: 19

The ‘‘trial'’ wavefuction for He atom is taken as where N is the normalization factor and Z ' is the variational parameter. Expression for the energy in terms of Z ' is found to be

Then the lowest value of the energy ( E ') for He atom i s _________________(in a.u .)
(Round off to two decimal places)


Solution:


For minimmn energy,

The minimum energy will be

QUESTION: 20

The average distance between the electron and nucleus of a He+ (singly ionised Heliumion) in the 1s state is

Solution:

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