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IIT JAM Physics MCQ Test 10 - Physics MCQ


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30 Questions MCQ Test - IIT JAM Physics MCQ Test 10

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IIT JAM Physics MCQ Test 10 - Question 1

If a beam of electrons impinges on an energy barrier of height 0.03 eV and of infinite width. Find the fraction of electrons reflected and transmitted at the barrier if the impinging electrons
are having energy 0.04 eV.

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 1

IIT JAM Physics MCQ Test 10 - Question 2

The probability of finding a particle inside the classical limits for an oscillator in its normal state is

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 2

The probability of finding the particle in classical region is given by
...(I)
where 
Energy of oscillator in ground state is given by  and classically, the total energy of the particle is
 (where A-Amplitude)
∴ 
⇒ 
Hence, equation (1) becomes


∴ 



≌ 0.84-84%.
i.e. the probability of finding the particle inside the classical limits in the normal state of the harmonic oscillator is 84%.

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IIT JAM Physics MCQ Test 10 - Question 3

The expected value of P for the wave function  is given

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 3

IIT JAM Physics MCQ Test 10 - Question 4

In rectangular box with sides L and 2L, the two states |2, 8 > and | 4, 4 > have

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 4

Using  ...(i)
for state |2,8,>

 ...(ii)
for state |4.4,>

 ...(iii)
E28 = E44
So the two states 12,8} and 14,4} have degeneracy and lack of symmetry.

IIT JAM Physics MCQ Test 10 - Question 5

The energy of a linear harmonic oscillator in third excited state is 0.1 eV. Then what is the frequency of vibration.

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 5

IIT JAM Physics MCQ Test 10 - Question 6

The wavefunctions of two identical particles in stated n and s are given by and respectively. The particles obey Maxwell-Boltzmann statistics. The state of the combined two-particle system is expressed as

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 6

Classical particle obey maxwell-Boltzmann statistics So. state of combined system = 

IIT JAM Physics MCQ Test 10 - Question 7

Two identical particles have to be distributed among three energy levels. Let rB, rr and rc represent the ratios of probability of finding two particles to that of finding one particle in a given energy state. The subscripts B. F and C correspond to whether the particles are bosons, fermions and classic particles, respectively. The, rB : rF: rc is equal to

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 7

Boson are indistingushable particles So in three energy state, they can be distributed as -

So, total micro state are 3 So, probability of finding two particle AB in which one particle is in one energy state is
 ...(i)
2) Fermins are also indistinguishable particles but according to Pauli exclusion principle they can not stay in one state so,  ...(ii)
3) Classical particle are distinguishable particle so they are distributed as -

So, there are 6 microstate, So probability
 ...(iii)
 

IIT JAM Physics MCQ Test 10 - Question 8

Ratio of the radius of 79Au197 nucleus with the radius of its innermost Bohr orbit is

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 8

We know R = R0 A10 
So, radius of the gold nucleus is 
R = 1.2 x 10-15m (197)1/3

Also, the radius of the first Bohr orbit for gold nuclei is 
Where Z0 = 5.292 * 10-11 m



IIT JAM Physics MCQ Test 10 - Question 9

What is the value of distance of closest approach of a 3 MeV proton to a gold nucleus.

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 9

The distance of closest approach by using the concept that at the point K.E. = P.E.
So 
Put the values,
Z1 = 79, Z2 = 1, K.E = 3 MeV
So   = 1.5 x 10-13m

IIT JAM Physics MCQ Test 10 - Question 10

Find the binding energy of lithium nucleus for the given data 
Mp= 1.00814 a.m.u
Mn = 1.0089 a.m.u.
MLi = 7.01822 a.m.u.

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 10

To find this, we use the formula
B.E = mass defect (in a.m.u.) * 931 MeV 
So, mass defect = 
We know that 3Li7 has 3 p rotons and 4 neutrons.  
So  Δm = 3 x 1.00814+4 * 1.0089-7.0182 
= 0.0418 (a.m.u.)
So B.E.= 0.0418 x 931 ≈ 39 MeV [Sine 1 a.m.u. = 931 MeV]

IIT JAM Physics MCQ Test 10 - Question 11

The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser is

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 11













IIT JAM Physics MCQ Test 10 - Question 12

A particle of mass m is confined in the potential

let the wave function of the particle be given by

where  are the eigenfunction s of the first excite d state and the second excited state respectively. The expectation value of the energy is

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 12

For half parabolic potential





IIT JAM Physics MCQ Test 10 - Question 13

The normalized ground state wavefunction of a hydrogen atom is given by   where a is the Bohr radius and r is the distance of the electron from the nucleus, located, at the origin. The expectation value  is

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 13





IIT JAM Physics MCQ Test 10 - Question 14

The ground state wavefunction for the hydrogen atom is given by  where ais the Bobr radius. The plot of the radial probability density, P(r) for the hydrogen atom in the ground state is 

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 14


The fround state is given by

Radial probability function

IIT JAM Physics MCQ Test 10 - Question 15

A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.
and the exitation energy is A x 10-32 J. The value of A is.

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 15


Hence the value of A is 4.69

*Multiple options can be correct
IIT JAM Physics MCQ Test 10 - Question 16

Which of the following nuclear reactions are possible?

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 16


So only a ,b are possible.

*Multiple options can be correct
IIT JAM Physics MCQ Test 10 - Question 17

A particle of mass m0 moves with speed c/√2, then its

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 17



Momentum p 

*Multiple options can be correct
IIT JAM Physics MCQ Test 10 - Question 18

A rod has length 100 cm. when the rod is in a satellite moving with a velocity that is one-half of the velocity of light relative to the laboratory, then

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*Multiple options can be correct
IIT JAM Physics MCQ Test 10 - Question 19

If the momentum of an electron is 10 times its rest mass times the speed light, then

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 19

Given, p = 10 m0c
Using 
So, 
Solving 
and 
Putting 


we get E = 9.22 x 10-13 J

*Multiple options can be correct
IIT JAM Physics MCQ Test 10 - Question 20

A particle of rest mass m is moving with a with a velocity 0.9c; then

Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 20

The relativistic mass

Given v = 0.9c 
(ii) Kinetic energy is given by

(iii) The expression   is correct only for low velocities which may be verified as follows




In this case we do not have u ≪ c, therefore it is incorrect to use 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 21

Let  Find the real value of A which normalises  in this equation.


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 21

The uncertainty in velocity

The uncertainty in momentum


Also Δp Δq =  or 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 22

An electron has a speed of 100 m/s with an accuracy of 0.005%. The uncertainty in position will be in x meter, 
the value of x is ?


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*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 23

Sum of all Eigen values of (pauli spin matrix) are___.


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 23




Eigen value  Ans.
Similarly for  


eigen value  Ans.
Similarly for  σz
eigen value 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 24

A particle is described by the wave function  where is the particle most likely to be found?


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 24

Normalization condition 
Therefore, we check whether 



Let, u 
So, 


So, the normalized wave function is

The particle is most likely to be found where  is maximum.
or  is maximum where 
or 
or 2x(1 + x 4) = 4x3 (1 + X2)
or 

The particle is most likely to found at

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 25

Determine the time [in day as measured by a clock at rest (on the rocket) taken by a rocket to reach a distant star and return to earth with a constant velocity  if the distance to the star is 4 light years (A light year is defined as the distance travelled by a light beam in vacuum in one year).


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 25

From the Lorentz transformation equation for time, we have

Here x = 2 x 4 light year
= 2 x 4 x 365 x 24 x 60 x 60 x c cm.
= 2.523 x 106 c,
where t is the time taken by the rocket to reach the star and back to the earth as measured by an observer in a stationary frame at earth and t' is the time measured by the clock in the moving rocket for the total journey
Now,  where 
∴ 
or  ...(ii)
Substituting the values of x and v in equation (2), we get


or 
= 2.523 x 106 sec  
or 29.2 day

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 26

Consider a system of eight non interacting, identical quantum particles of spin -3/2 in a one dimensional box of length L. The minimum excitation energy of the system , in units of  is____.


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 26

Spin 3/2 ⇒ degeneracy = (25 + 1) = 



Now minimum excitation energy

 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 27

A Two- dimensional square rigid box of side L contains eight non-interacting electrons at T =  ok. The mass of the electron is m. The ground state energy of the system of electrons, in units of   is ____.


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 27

Energy eigen value of two - dimensional system 


 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 28

An electron of mass m is confined to a one-dimensional box of length b. If it makes a radiative transition from second excited state to the ground state, the frequency of the photon emitted is _____


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 28


Since E = hv
For ground state  and for second state n2 = 3 

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 29

The de-Broglie wavelength for a He atom travelling at 1000 m/5 (typical speed at room temperature) i s __________ x10-12m•


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 29

We know that

*Answer can only contain numeric values
IIT JAM Physics MCQ Test 10 - Question 30

ln units of    the energy difference between levels corresponding to 3 and 2 node dimensional box of length l is ______.


Detailed Solution for IIT JAM Physics MCQ Test 10 - Question 30

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