Quantum Mechanics In Three Dimensions NAT


10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Quantum Mechanics In Three Dimensions NAT


Description
This mock test of Quantum Mechanics In Three Dimensions NAT for Physics helps you for every Physics entrance exam. This contains 10 Multiple Choice Questions for Physics Quantum Mechanics In Three Dimensions NAT (mcq) to study with solutions a complete question bank. The solved questions answers in this Quantum Mechanics In Three Dimensions NAT quiz give you a good mix of easy questions and tough questions. Physics students definitely take this Quantum Mechanics In Three Dimensions NAT exercise for a better result in the exam. You can find other Quantum Mechanics In Three Dimensions NAT extra questions, long questions & short questions for Physics on EduRev as well by searching above.
*Answer can only contain numeric values
QUESTION: 1

A stone with mass 1kg is whirled in a horizontal circle of radius 1m with a period of revolution equal to 1s. What value of orbital angular momentum quantum no. l describes this motion? (in 1034)


Solution:

The speed of the stone in its orbit is

Angular momentum = mvr = 1kg × 6.28 m/s × 1m
= 6.28 kg m2/s

For classical objects the quantum numbers are excessively big

The correct answer is: 5.96

*Answer can only contain numeric values
QUESTION: 2

Calculate the minimum value of for the stone mentioned in problem 4.


Solution:


The correct answer is: 0.9964

*Answer can only contain numeric values
QUESTION: 3

Calculate the average distance of an electron from the nucleus in the ground state of hydrogen atom is unit of a0.


Solution:


The correct answer is: 1.5

*Answer can only contain numeric values
QUESTION: 4

Find the level of degeneracy for particle in a 3d box with energy 


Solution:


level of degeneracy = 6
The correct answer is: 6

*Answer can only contain numeric values
QUESTION: 5

Find the value of the normalisation constant in the unit  of that normalizes the ground state wavefunction of the particle in a box of lengths L, 2L, 3L in  x, y and z directions respectively. Take  √3 = 1.732


Solution:

The probability density  Integration over the volume of the cube must be unity






The correct answer is: 1.15

*Answer can only contain numeric values
QUESTION: 6

Find the level of degeneracy for a 3 dimensional isotropic quantum harmonic oscillator of energy 


Solution:



(0, 0, 8) 3 states
(2, 2, 4) 3 states
(3, 3, 2) 3 states
(1, 1, 6) 3 states
(4, 4, 0) 3 states
=  3 × 5 = 15 states
Rest will give 6 states each
(0, 1, 7)(1, 2, 5)(4, 1, 3)(2, 0, 6)(0, 3, 5)
6 × 5 = 30
Total = 15 + 30 = 45 states
The correct answer is: 45

*Answer can only contain numeric values
QUESTION: 7

Consider two harmonic oscillators in 3 dimensions. For what ratio of angular frequencies will the first excited state of one oscillator have energy twice that of the second oscillator’s third excited state energy i.e find 


Solution:




The correct answer is: 3.6

*Answer can only contain numeric values
QUESTION: 8

Modeling a defect trap in a crystal as a 3d box with edge length 5Å, find the values of energy for an electron bound to the defect site, assuming the electron to be in the ground state. (in eV)


Solution:


= 0.0716 × 10-68 + 31 + 20
= 0.0714 × 10-17 Joules
= 0.0447 × 102 eV
= 4.5 eV
The correct answer is: 4.5

*Answer can only contain numeric values
QUESTION: 9

Find the probability of finding a particle in a 3d box of length L, in the volume 

(Assume the particle to be in the ground state).


Solution:




= 0.04
The correct answer is: 0.04

*Answer can only contain numeric values
QUESTION: 10

Calculate the probability that the electron in the ground state of hydrogen will be found outside the first Bohr radius in the unit e–2. Take


Solution:

The probability is found by integrating the radial probability density for this state from  a0  to ∞.


The correct answer is: 5

Similar Content

Related tests