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Quantum Chemistry - 1 - GATE Chemistry MCQ


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20 Questions MCQ Test GATE Chemistry Mock Test Series - Quantum Chemistry - 1

Quantum Chemistry - 1 for GATE Chemistry 2024 is part of GATE Chemistry Mock Test Series preparation. The Quantum Chemistry - 1 questions and answers have been prepared according to the GATE Chemistry exam syllabus.The Quantum Chemistry - 1 MCQs are made for GATE Chemistry 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Quantum Chemistry - 1 below.
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*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 1

The degeneracy of a 3-D S.H.O having energy 9/2hv is _________ (answer should be an integer).


Detailed Solution for Quantum Chemistry - 1 - Question 1

*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 2

The eigen value of x2e6y with respect to  is _________________ . (answer should be an integer)


Detailed Solution for Quantum Chemistry - 1 - Question 2

therefore, eigen value = 6

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*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 3

The number of energy states possible in the range   of a cubic box of side 'a'  is _____________   (answer should be an integer).


Detailed Solution for Quantum Chemistry - 1 - Question 3

Therefore, number if states is = 17

*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 4

the angular nodes present in the orbital respected by the wave function  is/are _________________.  (answer should be an integer)


Detailed Solution for Quantum Chemistry - 1 - Question 4

Angular node = l = Minimum power of r in radial part = 2

Quantum Chemistry - 1 - Question 5

The correct plot for second excited wave function of a 1-D SHO with the wave function

Detailed Solution for Quantum Chemistry - 1 - Question 5

At x = 0, ψ = -ve and node = 2

Quantum Chemistry - 1 - Question 6

An electron trapped in a 1-D box of length 1Å having energy 338 eV. This represents 

Detailed Solution for Quantum Chemistry - 1 - Question 6

En = +37.6 n2eV = 338.4eV

⇒ n2 = 9

⇒ n = 3

second excited state 

Quantum Chemistry - 1 - Question 7

What is the most probable distance from the proton to 1s in a speherical shell. The radial wave solution 

where , Z is the atomic number and a0 is the Bohr radius.

Detailed Solution for Quantum Chemistry - 1 - Question 7


since for maxima

Quantum Chemistry - 1 - Question 8

For a d-electron, the orbital angular momentum is 

Detailed Solution for Quantum Chemistry - 1 - Question 8

Quantum Chemistry - 1 - Question 9

the correct form of decay length in the tunneling through a barrier is 

Quantum Chemistry - 1 - Question 10

The correct statement (s) is/are

(I) π Bond energy of ethene is 2α

(II) π Bond energy of 1-3-Butadiene is 4.472 β

(III) π Bond energy of benzene is 8β

(Iv) π Bond energy of benzene is 6β

Detailed Solution for Quantum Chemistry - 1 - Question 10

(II) π Bond energy of 1-3-Butadiene is 4.472 β

(III) π Bond energy of benzene is 8β

Quantum Chemistry - 1 - Question 11

The K.E of elecron in the ground state of H-ato is 

Detailed Solution for Quantum Chemistry - 1 - Question 11

T.E = -13.6 eV  ..(i)

From equation (i)

⇒ P.E = -27.2 eV

Therefore, K.e = +13.6 eV

Quantum Chemistry - 1 - Question 12

consider a particle of mass 10-30 kg trapped in an infinitely deep potential well of width 0.59 nm. the value of k in ground state is approximately

Detailed Solution for Quantum Chemistry - 1 - Question 12

Quantum Chemistry - 1 - Question 13

The wave function for a quantum mechanical particle in a 1-D box of length 'l' is given by  The valur 'A' for a box of length 50 cm is

Detailed Solution for Quantum Chemistry - 1 - Question 13

Given that function   ∵ l= 50

*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 14

The zero point energy for a particle electron in 1-D box of length 1Å in units of n2 eV is ______________ (Round off to one decimal place)


Detailed Solution for Quantum Chemistry - 1 - Question 14

*Answer can only contain numeric values
Quantum Chemistry - 1 - Question 15

The number of energy levels possible in the range  of a cubic box of side 'a' is _______________ (answer should be an integer)


Detailed Solution for Quantum Chemistry - 1 - Question 15

Quantum Chemistry - 1 - Question 16

the minimum energy of a collection of 6 non-interacting electrons of spin -1/2 placed in a one dimensional infinite square well potential of width L is 

Detailed Solution for Quantum Chemistry - 1 - Question 16

The energy of a particle of mass 'm' in a one-dimension square well potential of width L is given by

only two electron with spin 1/2 can fill in the same state

(corresponding to minimum energy)

The minimum energy of the system is 

Quantum Chemistry - 1 - Question 17

For a particle of mass m confined in a rectangular box with side 3a and 4a. The energy and degeneracy of third excited state is

Detailed Solution for Quantum Chemistry - 1 - Question 17

Quantum Chemistry - 1 - Question 18

The molecular orbital of a  molecule is

The electronic charge density on the two hydrogen atoms are equal (0.5). The fround sate wave function  in zero and non-zero overlap approximately is [Given : SAB = 0.4584]

Detailed Solution for Quantum Chemistry - 1 - Question 18

Non-zero overloading


Solving both equation (i) and (ii)

c1 = 0.586

c2 = 0.586

Quantum Chemistry - 1 - Question 19

the valance bonding molecule orbital of a hydrogen chloride, molecule may be described as a linear combination of the hydrogen 1s and chlorine 3p atomic orbital 

calculate the probability of finding an electron in a 3p orbital ob chlorine

Detailed Solution for Quantum Chemistry - 1 - Question 19

Probability of finding on an electron in 3p-orbital

c1 = 0.23

c2 = 0.77

3p orbital probability = (0.77)2 = 0.59 = 59%

Quantum Chemistry - 1 - Question 20

One molecular orbital of a polar molecule AB has the form ​, where ψA and ψB are normalized atomic orbitals centred on A and B, respectively. The electron in this orbital is found on atom B with a probability of 80%. Neglecting the overlap between ψA and  ψB , a possible set of cA and cB is

Detailed Solution for Quantum Chemistry - 1 - Question 20

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