IIT JAM  >  Topic wise Tests for IIT JAM Physics  >  Postulates Of Quantum Mechanics NAT Download as PDF

Postulates Of Quantum Mechanics NAT


Test Description

10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Postulates Of Quantum Mechanics NAT

Postulates Of Quantum Mechanics NAT for IIT JAM 2023 is part of Topic wise Tests for IIT JAM Physics preparation. The Postulates Of Quantum Mechanics NAT questions and answers have been prepared according to the IIT JAM exam syllabus.The Postulates Of Quantum Mechanics NAT MCQs are made for IIT JAM 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Postulates Of Quantum Mechanics NAT below.
Solutions of Postulates Of Quantum Mechanics NAT questions in English are available as part of our Topic wise Tests for IIT JAM Physics for IIT JAM & Postulates Of Quantum Mechanics NAT solutions in Hindi for Topic wise Tests for IIT JAM Physics course. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free. Attempt Postulates Of Quantum Mechanics NAT | 10 questions in 45 minutes | Mock test for IIT JAM preparation | Free important questions MCQ to study Topic wise Tests for IIT JAM Physics for IIT JAM Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you?
*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 1

The wave function  where A and B are real constant, is a normalised eigenfunction of the Schrödinger equation for a particle of mass M and energy E in a one dimensional potential V(x) such that V(x) = 0 at x = 0. Find the value for V in units of 


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 1

Applying time independent Schrödinger equation

Substituting (2) in (1)

Putting V(x = 0) = 0  in (3)

The correct answer is: 0.5

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 2

In the spectrum of hydrogen, what is the ratio of the longest wavelength in the Lymann series to the longest is Balmer series ?


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 2

Energy emitted due to transition of electron -

Wherin

Longest wavelength in balmer series is corresponding to transition between 

Lets say it is 

Longest wavelength in lymen series is corresponding to transition between  2 ---> 1

Lets say it is 

=0.1852

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 3

In a photoelectric effect set up two metals with work function  φ1 and φ2 are used. For the same value of incident frequency, the stopping potential for metal 1 is twice that for metal 2. If the incident energy is 5eV and the φ1 = 1.5eV.  Find  φ2. (in eV)


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 3

Solution= 

eVs1=hv- Φ1

eVs2=hv- Φ2

eVs1= eVs2

eVs1/eVs2 = hv- Φ2/ hv- Φ1=1/2

2hv-2Φ= 1hv- Φ1

= hv+ Φ1

= 5+1.5

= 6.5eV

Φ= 3.25eV

The correct answer would be 3.25eV

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 4

A particle is in an infinite square well potential with walls at x = 0 and x = L. If the particle is in the state    where A is a constant, what is the probability that the particle is between x = L/3 and  x = 2L/3 upto 2 decimal places.


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 4



Now A2 = 2/L = from normalization of ψ
∴    Probability = 1/3 = 0.33
The correct answer is: 0.33

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 5

The figure shows one of the possible energy eigenfunction ψ(x) for a particle bouncing freely back and forth along the x-axis between impenetrable walls located at x ± a The potential energy equals zero for |x| < a. If the energy of the particle is 2eV when it is in the quantum state associated with its eigen function, what is its energy when it is in the quantum state of lowest energy (in eV)?


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 5

The number of nodes in a wavefunction determine the energy level. In this case there is just one node. Thus, this is E2. The lowest would be E1.
En = (const)n2
Since E2 = 2 = (constant) 4

The correct answer is: 0.5

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 6

What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillator


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 6

The correct answer is: 0.18

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 7

An electron in a metal encounters a barrier layer of height 6eV and thickness 0.5 nm. If the electron energy of 5eV, what is the probability of tunneling through the barrier?


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 7

We know,

With  E = 5eV  and  V0 = 16eV

With  a = 0.5 × 10–9 m,  m = 9.1 × 10–31 kg,  V0 = 6eV,  E = 5V   and 



Hence the percentage of probability of tunneling is 1.33.
The correct answer is: 1.33

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 8

The energy of an electron moving in one dimension in an infinitely high potential box of width 1Å.


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 8

The eigenvalue of energy


when the particle is in the least energy state (n = 1), the energy
with h = 6.62 × 10–34 Jsm = 9.1 × 10–31 kg and a = 1 × 10–10 m

After calculating,

The correct answer is: 37.62 eV

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 9

The solution of the schrödinger equation for the ground state of hydrogen is  where a0 is the Bohr radius and r is the distance from the origin. The most probable value of r  in units of a0.


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 9

For a hydrogen atom,

Now, for most probable r. We need to minimize the probability w.r.t. r.

Putting (2) in (1)

The correct answer is: 1

*Answer can only contain numeric values
Postulates Of Quantum Mechanics NAT - Question 10

The wave function of a particle is given by ψ(x) = Ce-ax,  -∞ < x < + ∞ where C and a are the some constants. The probability of finding the particle in the region  0 < x < ∞


Detailed Solution for Postulates Of Quantum Mechanics NAT - Question 10

The probability of finding the particle in the region  is 

Applying normalising condition i.e.,

The correct answer is: 0.5

Use Code STAYHOME200 and get INR 200 additional OFF
Use Coupon Code
Information about Postulates Of Quantum Mechanics NAT Page
In this test you can find the Exam questions for Postulates Of Quantum Mechanics NAT solved & explained in the simplest way possible. Besides giving Questions and answers for Postulates Of Quantum Mechanics NAT, EduRev gives you an ample number of Online tests for practice