# Solved papers for JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves JEE PYQ-Photo Electric Effect X-rays

### done JEE PYQ-Photo Electric Effect X-rays Total Questions - 70

• question_answer1) Sodium and copper have work functions $2.3$ eV and $4.5$ eV respectively. Then, the ratio of the wavelengths is nearest to     [AIEEE 2002]

A)
$1:2$

B)
$4:1$

C)
$2:1$

D)
$1:4$

• question_answer2) When ${{U}^{238}}$ nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is                                                [AIEEE 2003]

A)
$\frac{4\,u}{238}$

B)
$-\frac{4\,u}{238}$

C)
$\frac{4\,u}{234}$

D)
$-\frac{4\,u}{238}$

• question_answer3) Two identical, photocathodes receive light of frequencies ${{f}_{1}}$ and ${{f}_{2}}$. If the velocities of the photoelectrons (of mass m) coming out are respectively ${{v}_{1}}$ and ${{v}_{2}}$, then         [AIEEE 2003]

A)
${{v}_{1}}^{2}-{{v}_{1}}^{2}=\frac{2\,h}{m}({{f}_{1}}-{{f}_{2}})$

B)
${{v}_{1}}+{{v}_{2}}={{\left[ \frac{2\,h}{m}({{f}_{1}}+{{f}_{2}}) \right]}^{1/2}}$

C)
${{v}_{1}}^{2}+{{v}_{2}}^{2}=\frac{2\,h}{m}({{f}_{1}}+{{f}_{2}})$

D)
${{v}_{1}}-{{v}_{2}}={{\left[ \frac{2\,h}{m}({{f}_{1}}-{{f}_{2}} \right]}^{1/2}}$

• question_answer4) A radiation of energy E falls normally on d perfectly reflecting surface. The momentum transferred to the surface is            [AIEEE 2004]

A)
$E/c$

B)
$2E/c$

C)
$Ec$

D)
$E/{{c}^{2}}$

• question_answer5) According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal$Vs$the frequency, of the incident radiation gives a straight line whose slope    [AIEEE 2004]

A)
depends on the nature of the metal used

B)
depends on the intensity of the radiation

C)
depends both on the intensity of the radiation and the metal used

D)
is the same for all metals and independent of the intensity of the radiation

• question_answer6) The work function of a substance is$4.0\text{ }eV$. The longest wavelength of light that can cause photoelectron emission from this substance is approximately                        [AIEEE 2004]

A)
540 nm

B)
400 nm

C)
310nm

D)
220 nm

• question_answer7) A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 0.5m away, the number of electrons emitted by photocathode would                         [AIEEE 2005]

A)
decrease by a factor of 4

B)
increase by a factor of 4

C)
decrease by a factor of 2

D)
increase by a factor of 2

• question_answer8) If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor [AIEEE 2005]

A)
$\frac{1}{2}$

B)
2

C)
$\frac{1}{\sqrt{2}}$

D)
$\sqrt{2}$

• question_answer9) A nuclear transformation is denoted, by$X(n,\text{ }\alpha )\to _{3}^{7}Li$. Which of the following is the nucleus of element X?                [AIEEE 2005]

A)
$_{6}^{12}C$

B)
$_{5}^{10}B$

C)
$_{5}^{9}B$

D)
$_{4}^{11}Be$

• question_answer10) The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in [AIEEE 2006]

A)
ultraviolet region

B)
infrared region

C)
visible region

D)
X-ray region

• question_answer11) The time taken by a photoelectron to come out after the photon strikes is approximately [AIEEE 2006]

A)
${{10}^{-4}}s$

B)
${{10}^{-10}}s$

C)
${{10}^{-16}}s$

D)
${{10}^{-1}}s$

• question_answer12) The anode voltage of a photocell is kept fixed. The wavelength K of the light falling   on the cathode is gradually changed. The plate current I of the photocell varies as follows [AIEEE 2006]

A)

B)

C)

D)
None of these

• question_answer13) Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is                    [AIEEE 2007]

A)
v/c

B)
$y\ne 0$

C)
$x$

D)
$x$

• question_answer14)  This question contains Statement-1 and Statement -2 Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement-2: For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.                                        [AIEEE 2008]

A)
Statement -1 is true, Statement- 2 is true; Statement -2 is not a correct explanation for Statement-1

B)
Statement -1 is true, Statement- 2 is false

C)
Statement -1 is false, Statement- 2 is true

D)
Statement -1 is true, Statement- 2 is true; Statement -2 is a correct explanation for Statement-1

• question_answer15)  Directions: are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). Electrons accelerated by potential V are diffracted from a crystal. If $d=1\overset{o}{\mathop{A}}\,$ and $i={{30}^{o}}$, V should be about ($h=6.6\times {{10}^{-34}}Js$,${{m}_{e}}=9.1\times {{10}^{-31}}kg,\,e=1.6\times {{10}^{-19}}C$)                              [AIEEE 2008]

A)
500 V

B)
1000 V

C)
2000 V

D)
50 V

• question_answer16)  Directions: are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). If a strong diffraction peak is observed when electrons are incident at an angle 'I' from the normal to the crystal planes with distance d between them (see figure), de-Broglie wavelength${{\lambda }_{dB}}$ of electrons can be calculated by the relationship (n is an integer)                                                  [AIEEE 2008]

A)
$2\,d\sin i=n{{\lambda }_{dB}}$

B)
$d\cos i=n{{\lambda }_{dB}}$

C)
$d\sin i=n{{\lambda }_{dB}}$

D)
$2d\cos i=n{{\lambda }_{dB}}$

• question_answer17)  Directions: are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). In an experiment, electrons are made to pass through a narrow slit of width d comparable to their de Broglie wavelength. They are detected on a screen at a distance D from the slit (see figure). Which of the following graphs can be expected to represent the number of electrons N detected as a function of the detector position y (y = 0 corresponds to the middle of the slit)?          [AIEEE 2008]

A)

B)

C)

D)

• question_answer18) The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is:($hc=$ $1240\text{ }eV.nm$)[AIEEE 2009]

A)
$3.09\text{ }eV$

B)
$1.41\text{ }eV$

C)
$1.51\text{ }eV$

D)
$1.68\text{ }eV.$

• question_answer19)  Directions: contain Statement-1 and Statement-2 Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is${{V}_{0}}$and the maximum kinetic energy of the photoelectrons is${{K}_{max}}$. When the ultraviolet light is replaced by X-rays, both${{V}_{0}}$and${{K}_{max}}$ increase - Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because the range of frequencies present in the incident light.      [AIEEE 2010]

A)
Statement-1 is true, Statement-2 is false.

B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

D)
Statement-1 is false, Statement-2 is true.

• question_answer20) If a source of power 4 kW produces${{10}^{20}}$photons/second, the radiation belongs to a part of the spectrum called -          [AIEEE 2010]

A)
$\gamma -$rays

B)
X-rays

C)
ultraviolet rays

D)
microwaves

• question_answer21)  This question has Statement-1 and Statement-2 Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: A metallic surface is irradiated by a monochromatic light of frequency $\upsilon >{{\upsilon }_{0}}$ (the threshold frequency). The maximum kinetic energy and the stopping potential are ${{K}_{\max }}$ and ${{V}_{0}}$ respectively. If the frequency incident on the surface is doubled, both the${{K}_{\max }}$ and ${{V}_{0}}$ are also doubled. Statement-2: The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light. [AIEEE 2011]

A)
Statement-1 is false, Statement-2 is true

B)
Statement-1 is true, Statement-2 is false

C)
Statement-1 is true, Statement-2 is true and Statement-2 is a correct explanation for Statement-1

D)
Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1

• question_answer22)  This equation has statement 1 and Statement 2 Of the four choices given the Statements, choose the one that describes the two statements. Statement 1: Davisson-Germer experiment established the wave nature of electrons. Statement 2: If electrons have wave nature, they can interfere and show diffraction. [AIEEE 2012]

A)
Statement 1 is false, Statement 2 is true.

B)
Statement 1 is true, Statement 2 is false

C)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for statement 1

D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation o Statement 1

• question_answer23) A 10 kW transmitter emits radio waves of wavelength 500 m. The number of photons emitted per second by the transmitter is of the order of              [JEE ONLINE 12-05-2012]

A)
1037

B)
1031

C)
1025

D)
1043

• question_answer24)  This question has Statement 1 and Statement 2                              [JEE ONLINE 19-05-2012] Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A metallic surface is irradiated by a monochromatic light of frequency $\upsilon >{{\upsilon }_{0}}$ (the threshold frequency). If the incident frequency is now doubled, the photocurrent and the maximum kinetic energy are also doubled. Statement 2: The maximum kinetic energy of photoelectrons emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends only on the intensity of the incident light.

A)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B)
Statement 1 is false. Statement 2 is true.

C)
Statement 1 is true, Statement 2 is false.

D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

• question_answer25) Photoelectrons are ejected from a metal when light of frequency $\upsilon$ falls on it. Pick out the wrong statement from the following.                           [JEE ONLINE 26-05-2012]

A)
No electrons are emitted if o is less than W/h, where W is the work function of the metal

B)
The ejection of the photoelectrons is instantaneous.

C)
The maximum energy of the photoelectrons is $h\upsilon .$

D)
The maximum energy of the photoelectrons is independent of the intensity of the light.

• question_answer26) The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:            [JEE MAIN 2013]

A)

B)

C)

D)

• question_answer27) Orbits of a particle moving in a circle are such that the perimeter of orbit equals an integer number of de - Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to: [JEE ONLINE 22-04-2013]

A)
${{n}^{2}}$

B)
$n$

C)
${{n}^{1/2}}$

D)
${{n}^{1/4}}$

• question_answer28) Electrons are accelerated through a potential difference V and protons are accelerated through a potential difference 4 V. The de-Broglie wavelengths are  ${{\lambda }_{e}}$ and ${{\lambda }_{\operatorname{p}}}$ for electrons and protons respectively. The ratio of $\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}$ is given by:              (given${{\operatorname{m}}_{e}}$is mass of electron and${{\operatorname{m}}_{\operatorname{p}}}$is mass of proton)                              [JEE ONLINE 23-04-2013]

A)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{\operatorname{p}}}}{{{\operatorname{m}}_{\operatorname{e}}}}}$

B)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}$

C)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\frac{1}{2}\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}$

D)
$\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=2\sqrt{\frac{{{\operatorname{m}}_{\operatorname{P}}}}{{{\operatorname{m}}_{e}}}}$

• question_answer29)  In an experiment on photoelectric effect, a student plots stopping potential ${{V}_{0}}$ against reciprocal of the wavelength $\lambda$ of the incident light for two different metals A and B These are shown is the figure. Looking at the graphs, you can most appropriately say that: [JEE ONLINE 25-04-2013]

A)
Work function of metal B is greater that that of metal A

B)
For light of certain wavelength falling on both metal, maximum kinetic energy of electrons emitted from A will be greater than those emitted from B.

C)
Work function of metal A is greater than that of metal B

D)
Students data is not correct

• question_answer30) A copper ball of radius 1 cm and work function 4.47 eV us irradiated with ultraviolet radiation of wavelength$2500{{\operatorname{A}}_{\circ }}$. The effect of irradiation results in the emission of electrons form the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is:                                                                    [JEE ONLINE 25-04-2013]

A)
$5.5\times {{10}^{-13}}C$

B)
$7.5\times {{10}^{-13}}C$

C)
$4.5\times {{10}^{-12}}C$

D)
$2.5\times {{10}^{-11}}C$

• question_answer31) The radiation corresponding to $3\to 2$transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times {{10}^{-4}}T.$If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to: [JEE MAIN 2014]

A)
0.8 eV

B)
1.6 eV

C)
1.8 eV

D)
1.1 eV

• question_answer32) For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship? [JEE ONLINE 09-04-2014]

A)
an electron

B)
a proton

C)
an$\text{ }\!\!\alpha\!\!\text{ }$particle

D)
a dust particle

• question_answer33) A photon of wavelength l is scattered from an electron, which was at rest. The wavelength shift $\Delta \lambda$ is three times of $\lambda$ and the angle of scattering $\theta$ is 60°. The angle at which the electron recoiled is $\phi .$ The value of tan $\phi$ is: (electron speed is much smaller than the speed of light) [JEE ONLINE 11-04-2014]

A)
0.16

B)
0.22

C)
0.25

D)
0.28

• question_answer34) A beam of light has two wavelengths of 4972Å and 6216Å with a total intensity of $3.6\times {{10}^{-3}}W{{m}^{-2}}$ equally distributed among the two wavelengths. The beam falls normally on an area of 1 $c{{m}^{2}}$ of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2s is approximately:          [JEE ONLINE 12-04-2014]

A)
$6\times {{10}^{11}}$

B)
$9\times {{10}^{11}}$

C)
$11\times {{10}^{11}}$

D)
$15\times {{10}^{11}}$

• question_answer35)  Match List - I (Experiment performed) with List-II (Phenomena discovered/associated) and select the correct option from the options given below the lists:   [JEE ONLINE 19-04-2014] List I List-II (1) Davisson and Germer experiment (i) Wave nature of electrons (2) Millikans oil drop experiment (ii) Charge of an electron (3) Rutherford experiment (iii) Quantization of energy levels (4) Franch-Hertz experiment (iv) Existence of nuleus

A)
(1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)

B)
(1)-(i), (2)-(ii), (3)-(iv), (4)-(iii)

C)
(1)-(iii), (2)-(iv), (3)-(i), (4)-(ii)

D)
(1)-(iv), (2)-(iii), (3)-(ii), (4)-(i)

• question_answer36)  Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list:                                      [JEE MAIN 2015] List-I List-II Franck-Hertz Experiment (i) Particle nature of light Photo-electric experiment (ii) Discrete energy levels of atom Davison - Germer Experiment (iii) Wave nature of electron (iv) Structure of atom

A)
- (ii) - (i) - (iii)

B)
- (iv) - (iii) - (ii)

C)
- (i) - (iv) - (iii)

D)
- (ii) - (iv) - (iii)

• question_answer37)  de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to [JEE ONLINE 10-04-2015] $(|e|=1.6\times {{10}^{-19}}C,$${{m}_{e}}=9.1\times {{10}^{-31}}kg,$                          $h=6.6\times {{10}^{-34}}Js)$

A)
$0.5{\AA}$

B)
$1.7{\AA}$

C)
$2.4{\AA}$

D)
$1.2{\AA}$

• question_answer38) Let ${{N}_{\beta }}$ be the number of $\beta$ particles emitted by 1 gram of $N{{a}^{24}}$ radioactive nuclei (half-life = 15 hrs) in 7.5 hours, ${{N}_{\beta }}$ is close to (Avogadro number$=6.023\times {{10}^{23}}/g.$mole): [JEE MAIN 11-04-2015]

A)
$6.2\times {{10}^{21}}$

B)
$7.5\times {{10}^{21}}$

C)
$1.25\times {{10}^{22}}$

D)
$1.75\times {{10}^{22}}$

• question_answer39) Radiation of wavelength $\lambda ,$is incident on a photocell. The fastest emitted electron has speed v. If the wavelength of changed to$\frac{3\lambda }{4},$ the speed of the fastest emitted electron will be:- [JEE MAIN - I 3-4-2016]

A)
$=v{{\left( \frac{3}{5} \right)}^{1/2}}$

B)
$>v{{\left( \frac{4}{3} \right)}^{1/2}}$

C)
$<v{{\left( \frac{4}{3} \right)}^{1/2}}$

D)
$=v{{\left( \frac{4}{3} \right)}^{1/2}}$

• question_answer40) When photons of wavelength ${{\lambda }_{1}}$, are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength ${{\lambda }_{2}}$are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength ${{\lambda }_{3}}.$is used then find the stopping potential for this case         [JEE ONLINE 09-04-2016]

A)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{3}{2{{\lambda }_{1}}} \right]$

B)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{{{\lambda }_{2}}}-\frac{3}{{{\lambda }_{1}}} \right]$

C)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]$

D)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}-\frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]$

• question_answer41) A photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda$ and $\frac{\lambda }{3}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 time that in the first case, the work function of the surface is:                              [JEE ONLINE 10-04-2016]

A)
$\frac{3hc}{\lambda }$

B)
$\frac{hc}{\lambda }$

C)
$\frac{hc}{3\lambda }$

D)
$\frac{hc}{2\lambda }$

• question_answer42) An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If${{\lambda }_{\min }}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of $\log {{\lambda }_{\min }}$ with log V is correctly represented in:  [JEE Main 2017]

A)

B)

C)

D)

• question_answer43) A particle A of mass m and initial velocity v collides with a particle B of mass$\frac{m}{2}$which is at rest. The collision is head on, and elastic. The ratio of the deBroglie wavelengths ${{\lambda }_{A}}$to ${{\lambda }_{B}}$ after the collision is: [JEE Main 2017]

A)
$\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{2}{3}$

B)
$\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}$

C)
$\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}$

D)
$\frac{{{\lambda }_{A}}}{{{\lambda }_{_{B}}}}=2$

• question_answer44) The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be  [JEE Online 08-04-2017]

A)
more than $\sqrt{3}v$

B)
equal to $\sqrt{3}v$

C)
v

D)
less than $\sqrt{3}v$

• question_answer45)  A laser light of wavelength 660 nm is used to weld Retina detachment. If a laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are - [JEE Online 09-04-2017] [Take Planck's constant $h=6.62\,\times {{10}^{-34}}Js$]

A)
${{10}^{22}}$

B)
${{10}^{19}}$

C)
${{10}^{20}}$

D)
${{10}^{18}}$

• question_answer46) An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${{\lambda }_{n}},\,\,{{\lambda }_{g}}$ be the de Broglie wavelength of the electron in the ${{\text{n}}^{\text{th}}}$  state and the ground state respectively. Let ${{\Lambda }_{n}}$ be the wavelength of the emitted photon in the transition from the ${{n}^{th}}$ state to the ground state. For large n, (A, B are constants) [JEE Main Online 08-04-2018]

A)
$\Lambda _{n}^{2}\approx A+B\lambda _{n}^{2}$

B)
$\Lambda _{n}^{2}\approx \lambda$

C)
${{\Lambda }_{n}}\approx A+\frac{B}{\lambda _{n}^{2}}$

D)
${{\Lambda }_{n}}\approx A+B{{\lambda }_{n}}$

• question_answer47) Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths  are ${{\lambda }_{1}}$ and ${{\lambda }_{2}}$, their de Broglie wavelength in the frame of reference attached to their centre of mass is:                          [JEE Online 15-04-2018]

A)
${{\lambda }_{CM}}={{\lambda }_{1}}={{\lambda }_{2}}$

B)
$\frac{1}{{{\lambda }_{CM}}}=\frac{1}{{{\lambda }_{1}}}+\frac{1}{{{\lambda }_{2}}}$

C)
${{\lambda }_{CM}}=\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{{{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}}}$

D)
${{\lambda }_{CM}}=\left( \frac{{{\lambda }_{1}}+{{\lambda }_{2}}}{2} \right)$

• question_answer48) If the de Broglie wavelengths associated with a proton and an $\alpha -particle$are equal, then the ratio of velocities of the proton and the $\alpha -particle$ will be: [JEE Online 15-04-2018 (II)]

A)
$1:4$

B)
$1:2$

C)
$4:1$

D)
$2:1$

• question_answer49) The de-Broglie wavelength$({{\lambda }_{B}})$associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state$({{\lambda }_{G}})$by [JEE Main Online 16-4-2018]

A)
${{\lambda }_{B}}={{\lambda }_{G/3}}$

B)
${{\lambda }_{B}}={{\lambda }_{G/2}}$

C)
${{\lambda }_{B}}=2{{\lambda }_{G}}$

D)
${{\lambda }_{B}}=3{{\lambda }_{G}}$

• question_answer50) In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of  m, the minimum electron required is close to- [JEE Main 10-Jan-2019 Morning]

A)
25 ke V

B)
500 ke V

C)
100 ke V

D)
1 ke V

• question_answer51) A metal plate of area  is illuminated by a radiation of intensity. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only  of it produces photo electrons. The number of  emitted photoelectrons per second and their maximum energy, respectively, will be- [JEE Main 10-Jan-2019 Evening]

A)
and 10 eV

B)
and 5 eV

C)
and 5 eV

D)
and 5 eV

• question_answer52)  If the de Broglie wavelength of an electron is equal to  times the wavelength of a photon of frequency then the speed of electron is equal to-                                       [JEE Main 11-Jan-2019 Morning] (Speed of light Plancks constant Mass of electron)

A)

B)

C)

D)

• question_answer53) In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to [JEE Main 11-Jan-2019 Evening]

A)
2.0 V

B)
0.5 V

C)
1.0 V

D)
1.5 V

• question_answer54) In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to- [JEE Main 12-Jan-2019 Evening]

A)
220 nm

B)
1700 nm

C)
250 nm

D)
2020 nm

• question_answer55) When a certain photosensitive surface is illuminated with monochromatic light of frequency u, the stopping potential for the photo current isWhen the surface is illuminated by monochromatic light of frequencythe stopping potential is The threshold frequency for photoelectric emission is- [JEE Main 12-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer56) Two particles move at right angle to each other. Their de-Broglie wavelengths are and  respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength , of the final particle, is given by : [JEE Main 8-4-2019 Morning]

A)

B)

C)

D)

• question_answer57) A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths  and  respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-              [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer58) A  ion is in its first excited state. Its ionization energy is :- [JEE Main 9-4-2019 Afternoon]

A)
6.04 eV

B)
13.60 eV

C)
54.40 eV

D)
48.36 eV

• question_answer59) In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV)  [JEE Main 10-4-2019 Morning]

A)
1.5 eV

B)
4.5 eV

C)
15.1 eV

D)
3.0 eV

• question_answer60) A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant  speed of light ] [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer61)  The stopping potential (in volt) as a function of frequency (v) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given : Planck's constantelectron charge ) [JEE Main Held on 12-4-2019 Morning]

A)
1.95 eV

B)
1.82 eV

C)
1.66 eV

D)
2.12 eV

• question_answer62) The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, of the photons emitted in this process is : [JEE Main 12-4-2019 Afternoon]

A)
9/7

B)
7/5

C)
27/5

D)
20/7

• question_answer63) Consider an electron in a hydrogen atom, revolving in its second excited state (having radius ). The de-Broglie wavelength of this electron is : [JEE Main 12-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer64) A beam of electromagnetic radiation of intensity $6.4\times {{10}^{5}}W/c{{m}^{2}}$ is comprised of wavelength, $\lambda =310\text{ }nm$. It falls normally on a metal (work function $\varphi =2\text{ }eV$) of surface area of $1\text{ }c{{m}^{2}}$. If one in ${{10}^{3}}$ photons ejects an electron, total number of electrons ejected in 1 s is ${{10}^{x}}$. $(hc=1240\text{ }eVnm,\text{ }1\text{ }eV=1.6\times {{10}^{19}}J)$, then x is _______.           [JEE MAIN Held on 07-01-2020 Morning]

• question_answer65) When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${{T}_{A}}$eV and de-Broglie wavelength${{\lambda }_{A}}.$ The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy $4.50\text{ }eV$is ${{T}_{B}}=\left( {{T}_{A}}1.5 \right)eV.$ If the de-Broglie wavelength of these photoelectrons ${{\lambda }_{B}}=2{{\lambda }_{A}},$ then the work function of metal B is: [JEE MAIN Held On 08-01-2020 Morning]

A)
$1.5\text{ }eV$

B)
$4\text{ }eV$

C)
$\text{3 }eV$

D)
$\text{2 }eV$

• question_answer66) An electron (mass m) with initial velocity $\vec{v}={{v}_{0}}\,\hat{i}+{{v}_{0}}\,\hat{j}$ is in an electric field $\vec{E}=-{{E}_{0}}\hat{k}$. If ${{\lambda }_{0}}$ is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time t is given by [JEE MAIN Held on 08-01-2020 Evening]

A)
$\frac{{{\lambda }_{0}}}{\sqrt{1+\frac{{{e}^{2}}E_{0}^{2}{{t}^{2}}}{{{m}^{2}}v_{0}^{2}}}}$

B)
$\frac{{{\lambda }_{0}}\sqrt{2}}{\sqrt{1+\frac{{{e}^{2}}{{E}^{2}}{{t}^{2}}}{{{m}^{2}}v_{0}^{2}}}}$

C)
$\frac{{{\lambda }_{0}}}{\sqrt{1+\frac{{{e}^{2}}{{E}^{2}}{{t}^{2}}}{2{{m}^{2}}v_{0}^{2}}}}$

D)
$\frac{{{\lambda }_{0}}}{\sqrt{2+\frac{{{e}^{2}}{{E}^{2}}{{t}^{2}}}{{{m}^{2}}v_{0}^{2}}}}$

• question_answer67) A particle moving with kinetic energy E has de Broglie wavelength$\lambda$. If energy $\Delta E$ is added to its energy, the wavelength become$\lambda /2$. Value of $\Delta E$, is : [JEE MAIN Held on 09-01-2020 Morning]

A)
4E

B)
E

C)
2E

D)
3E

• question_answer68) Radiation, with wavelength 6561$\overset{\text{o}}{\mathop{\text{A}}}\,$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3\text{ }\times \text{ }{{10}^{4}}$T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to [JEE MAIN Held on 09-01-2020 Morning]

A)
1.6 eV

B)
1.1 eV

C)
0.8 eV

D)
1.8 eV

• question_answer69) An electric dipole of moment $\vec{p}-=\left( -\hat{i}-3\hat{j}+2\hat{k} \right)\times {{10}^{-29}}$C.m is at the origin (0, 0, 0). The electric field due to this dipole at $\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}$(note that $\vec{r}.\vec{p}=0$) is paralled to [JEE MAIN Held on 09-01-2020 Morning]

A)
$\left( -\hat{i}-3\hat{j}+2\hat{k} \right)$

B)
$\left( +\hat{i}-3\hat{j}-2\hat{k} \right)$

C)
$\left( -\hat{i}+3\hat{j}-2\hat{k} \right)$

D)
$\left( +\hat{i}+3\hat{j}-2\hat{k} \right)$

• question_answer70) An electron of mass m and magnitude of charge $\left| e \right|$initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is [JEE MAIN Held on 09-01-2020 Evening]

A)
$-\frac{h}{|e|E\sqrt{t}}$

B)
$\frac{-h}{|e|E{{t}^{2}}}$

C)
$\frac{|e|Et}{h}$

D)
$-\frac{h}{|e|Et}$