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IIT JAM Physics Mock Test - 8 - Physics MCQ


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30 Questions MCQ Test - IIT JAM Physics Mock Test - 8

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IIT JAM Physics Mock Test - 8 - Question 1

How much energy must be given to an election to accelerate it to 0.95c?

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 1

Use the mass-increase formula.


E = (m - m0)c2
= [(29.1 - 9.1) (10-31)] (9 x 1016
= 1.8 x 10-13 J = 1.125 MeV

IIT JAM Physics Mock Test - 8 - Question 2

The de-Broglie wavelength of a proton and an α - paiticle are equal. The ratio of their velocities is:

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 2

Every particle of mass m moving with velocity v is associated with a wave of wavelength given as
 Planck's constant
The wavelength for proton

and the wavelength for He

Since,

⇒  
Since 2He4 has four nucleons so m = 4mP
Thus, (iii) 

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IIT JAM Physics Mock Test - 8 - Question 3

Let the potential energy of a hydrogen atom in the ground state be zero. Then its energy in the first excited state will be

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 3

Since we assume the potential energy to be zero in the ground state . So Total energy = U + K = Kinetic energy 
Since P E = U = 0
∴ Total energy = 13.6ev (in ground state)
If the potential energy is not assigned a zero value, then the total energy is - 13.6ev .
So we conclude that making potential energy zero increases the value of total energy by 13.6 - ( - 13.6) = 27.2ev 
Now actual energy in second orbit = - 3.4ev
Hence new value is ( - 3.4 ev + 27.2 ev) = 23.8ev

IIT JAM Physics Mock Test - 8 - Question 4

A clock keeps correct time, with what speed should it be moved to an observer so that it may appear to loose 5 minutes in 24 hours?

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 4

We use 
where is proper time = 1440 minutes in a day and t = 1445 minutes measured by a stationary obseiver.
So 
So 
or 
 

IIT JAM Physics Mock Test - 8 - Question 5

The rate of radiation of a black body at 00C is E Watt. Then the rate of radiation of this black body at 2730C will be :

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 5

By Stefan's law, rate of emission is proportional to fourth power of the absolute temperature i.e.,

⇒  ⇒ 
Here.  T1= 0 + 273 = 273. T2 = 273 + 273 = 2 x 273
SO, 

IIT JAM Physics Mock Test - 8 - Question 6

A harmonic oscillator has the wave function   is the eigenfunction belonging to the nth energy eigenvalue  The expectation value <E> of energy for the state ψ(x,t) is

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 6

 for Harmonic oscillator energy eigen value is 





IIT JAM Physics Mock Test - 8 - Question 7

Consider a quantum mechanical system with three linear operators  which are related by  Where  is the unit operator. If  the  must be 

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 7



IIT JAM Physics Mock Test - 8 - Question 8

Electric field component of an electro magnetic radiation varies with time as  where a is a constant and the values of the ω and  respectively. This radiation falls on a metal of work function 2 eV. The maximum kinetic Energy of photoelectrons is.

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 8



The maximum frequency of photon = 

IIT JAM Physics Mock Test - 8 - Question 9

The electrons x and y are moving with velocities 0.1 C and 0.8C respectively. The ratio of energies ΔEX / ΔEy required to increase the speed of each by 0.1 C is given approximately by

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 9





IIT JAM Physics Mock Test - 8 - Question 10

A particle A of mass mA decays into two particles, one of which is B with mass mB and the other massless. The magnitude of the momentum of particle B using relativistic kinematics in the first-frame of the particle A is

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


According to law of conservation of linear momentum. The momentum of particle B and massless particle are equal in magnitude and opposite is sign. Let their momentum be p.


Momentum of particle B is rest frame of particle a is same as that of massless particle

IIT JAM Physics Mock Test - 8 - Question 11

A driver is being fined for overlooking a red signal. The driver claimed that instead of red colour (v0 = 4.8 * 1014 Hz) he saw green (v = 5.6 * 1014 Hz) because of Dopper effect. The judge fined the driver for speed at the rate of Rs. 1/- for each km/h he exceeded the speed limit of 80 km/h. What is the fine?

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 11


 = 4.59 107 m /sec. = 1.65 x108 km/h
1 m/sec. = 3.6 km/hr
fine = 1.65 x 108 - 80 = 164999920/-

IIT JAM Physics Mock Test - 8 - Question 12

In a Devisson - Germer experiment a collimated beam of electrons of energy 54eV at a normal incidence on a given crystal, shows a peak appears at the same value of reflection angle, then the energy of the neutrons must be

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 12

In Davission - Germer experiment when electron is replaced by neutron, then same peak at a reflection angle of 40° is obtained which shows the same wavelength of e- and neutron.



IIT JAM Physics Mock Test - 8 - Question 13

The photo electric threshold of certain metal is 2750 A°. Find the maximum kinetic energy of the electrons. 

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 13

Work function 

Maximum kinetic energy

IIT JAM Physics Mock Test - 8 - Question 14

The velocity of an electron in the ground state of a hydrogen atom is VH. If Vp be the velocity of an electron in the ground state of positronium, then

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 14

H-atom having one electron in its ground state. So. having VH velocity and positronium is the electron category, that is a particle having mass equal to electron but charge opposite in nature and same magnitude. 
qp = 1.6 x 10-19
Mp = 9.1 x 10-31kg
So, velocity of positronium (Vp) is equal to the velocity of electron in H-atom VH
Vp = VH

IIT JAM Physics Mock Test - 8 - Question 15

A beam of atoms moving in a certain direction can be slowed down if they absorb photons from a laser beam moving in the opposite direction and subsequently spontaneously emit photons isotropically. For a beam of sodium atoms (mass number A = 23) with speed 600 m/sec. If a laser beam of wavelength 589 nm is used the number of such absorption and emission cycles needed to bring a sodium atom to rest would be approximately________

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 15

Photon momentum P = h/λ (for one cycle)
P must be equal to mV.
If n is no. of cycles then

m = 23 x 1.66 x 10-27 kg = 3.818 x 10-26kg 
V = 600 m/sec 


n = 2.1 x 104

IIT JAM Physics Mock Test - 8 - Question 16

An α-particle and a proton are fired through the same magnetic field which is perpendicular to their velocity vectors. The α-particle and the proton move such that radius of curvature of their path is same. What is the ratio of their de-Broglie wavelengths?

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 16

Magnetic force experienced by a charged particle in magnetic field is given by

 ⇒ mv = qBr

 

IIT JAM Physics Mock Test - 8 - Question 17

In a collision between a photon and a free electron, which is correct, if all the photon energy were transferred to the electron.

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 17

Let E1 = hv energy of photon
 momentum of photon
 energy of electron
P2 = momentum of electron 
If all energy is to be transferred to the electron hv 
Electron momentum

IIT JAM Physics Mock Test - 8 - Question 18

Denote the computer of two matrices A and by [A, B] = AB - BA and anti commutator by {A,B} = AB + BA 
If {A.B} = 0 we can write [A,B,C]

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 18

Given that {A, B} = 0 or AB = - BA 
⇒ [A.B.C] = [A.B] C + B [A.C] = ABC - BAC + BAC - BCA 
= ABC - BCA = - BAC - BCA = - B (AC + CA) 
[A.BC] = - B {A.C}

IIT JAM Physics Mock Test - 8 - Question 19

The activity of a radioactive sample is decreased by 25% of the initial value after 30 days. The half - life (in days) of the sample is approximately

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 19




Half life 
Half life  

IIT JAM Physics Mock Test - 8 - Question 20

Five 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 is

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 20


Energy of the lowest energy state of system


IIT JAM Physics Mock Test - 8 - Question 21

The frequency of electron in Bohr orbit is given by f1 revolutions/sec. The frequency of electron in the n-th orbit for n > 1 is

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 21

We know that
Radius of Bohr atom is 

and velocity of electron

Time period of cycle


T α n3
⇒ frequency of electron = f1/h3

IIT JAM Physics Mock Test - 8 - Question 22

An electron is moving inside a uniformly charged sphere with total charge +ve. The uncertainty principle ΔPxΔx ≥ n is used for finding the smallest radius rmin of the charged sphere such that the kinetic energy of the electron is equal to its potential energy on the surface of the sphere. The rmin is approximately in the range    .

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 22

Potential energy of interaction between electron and sphere






IIT JAM Physics Mock Test - 8 - Question 23

The Compton effect experiment photons of energy h v around material of atomic number Z. The change in wavelength can be

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 23

The change in wavelength

= 0.0243(1 - cos φ) A0
Therefore the change is easily detectable in case of X-ray (wavelength ≈ 1 A0)

IIT JAM Physics Mock Test - 8 - Question 24

1.5 mW of 400 nm light is directed at a photo electric cell. If 0.1 % of the incident photon produce e-s. all the photo e- s reach the opposite plate, so the current in the photo cell is equal to______ .

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 24

Since  ...(i)
⇒ n/t ⇒ no. of photo e-s produced per second.
Now let the no. of photons hitting the photo cell per second will be n 
nhv = 1.5 x 10-3 Watt


No. of photo e- produced per second is

= 3 x 1011 e/sec.
Using equation (1)
I = 3 x 1011 x 1.6 x 10-19
I = 4.8 x 10-7 amp = .48 μ amp.

IIT JAM Physics Mock Test - 8 - Question 25

In a hydrogen - like atom, an election is the ground state requires 476 ev to reach an excited level with quantum number 2n. If it makes a transition from this level to a lower level with quantum number n, it emits a photon of energy 40.8 eV. Find the atomic number Z of the element

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 25

For hydrogen like atom 

Now. it requires 476 eV to reach 2n level from ground state 
E2n- E1 = 476
 ...(i)

It emits energy of 40.8 eV while making transition from 2n level to n level 
E2n - En = 40.8

 ...(ii)
Dividing (1) and (2)

n = 3
Putting n = 3 in (2) we get z = 6

IIT JAM Physics Mock Test - 8 - Question 26

The speed of an electron, whose de Broglie wavelength is equal to its Compton wavelength, is (C is the speed of light)

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 26



IIT JAM Physics Mock Test - 8 - Question 27

A neutron of mass mn = 10-27 kg is moving inside a nucleus. Assume the nucleus to be a cubical box of size 10-14 m with impenetrable walls. Take Js and 1 MeV ≈ 10-13 J . An estimate of the energy in Mev of the neutron is

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 27





IIT JAM Physics Mock Test - 8 - Question 28

The longest wavelength in the Balmer series of hydrogen atom is given as 656 nm positronium can be considered as a system of an electron and a positron in which both these particles orbit each other. What will be the longest wavelength in the lyman series for positronium?

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 28

The expression of wavelength emitted when an electron makes a transition from nth level to mth level is given by

for Balmer series m = 2

The value for n for longest wavelength will be 3



for positronium mass m will be replaced with reduced mass μ. 

Rydberg constant for H - atom

Rydberg constant for positronium

for lyman series 
for longest wavelength n = 2


IIT JAM Physics Mock Test - 8 - Question 29

Positronium is a hydrogen like bound state of a position and electron. If the nth energy level of hydrogen atoms is given by  the nth energy  of the positronium will be equal to

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 29

Mass of e+ (positron) = mass of e- (electron) = m
so, Reduced mass of positronium 
m = m/2
so, if 


IIT JAM Physics Mock Test - 8 - Question 30

A particle has rest mass m0 and momentum m0c, where c is the velocity of light. The total energy and the velocity of the particle are respectively.

Detailed Solution for IIT JAM Physics Mock Test - 8 - Question 30

That energy of a relativistic particle is given by
E2 = p2C2 + m20c

Again, momentum of the particle 
⇒ 
⇒ 

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