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Dual Nature of Radiation

209 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
2022 JEE Mains MCQ
JEE Main 2022 (Online) 28th June Morning Shift

The de Broglie wavelengths for an electron and a photon are $\lambda$e and $\lambda$p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?

A.
${\lambda _p} \propto \lambda _e^2$
B.
${\lambda _p} \propto {\lambda _e}$
C.
${\lambda _p} \propto \sqrt {{\lambda _e}} $
D.
${\lambda _p} \propto \sqrt {{1 \over {{\lambda _e}}}} $
2022 JEE Mains MCQ
JEE Main 2022 (Online) 27th June Morning Shift

An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $({\lambda _\alpha }:{\lambda _{C12}})$ is :

A.
$1:\sqrt 3 $
B.
$\sqrt 3 :1$
C.
$3:1$
D.
$2:\sqrt 3 $
2022 JEE Mains MCQ
JEE Main 2022 (Online) 26th June Evening Shift

A metal surface is illuminated by a radiation of wavelength 4500 $\mathop A\limits^o $. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90$^\circ$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :

A.
1.36 eV
B.
1.69 eV
C.
2.78 eV
D.
2.23 eV
2022 JEE Mains MCQ
JEE Main 2022 (Online) 26th June Morning Shift

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?

A.
${{{E_e}} \over {{E_{ph}}}} = {{2c} \over v}$
B.
${{{E_e}} \over {{E_{ph}}}} = {v \over {2c}}$
C.
${{{p_e}} \over {{p_{ph}}}} = {{2c} \over v}$
D.
${{{p_e}} \over {{p_{ph}}}} = {v \over {2c}}$
2022 JEE Mains MCQ
JEE Main 2022 (Online) 25th June Evening Shift

A proton, a neutron, an electron and an $\alpha$ particle have same energy. If $\lambda$p, $\lambda$n, $\lambda$e and $\lambda$a are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following :

A.
$\lambda$p = $\lambda$n > $\lambda$e > $\lambda$a
B.
$\lambda$a < $\lambda$n < $\lambda$p < $\lambda$e
C.
$\lambda$e < $\lambda$p = $\lambda$n > $\lambda$a
D.
$\lambda$e = $\lambda$p = $\lambda$n = $\lambda$a
2022 JEE Mains MCQ
JEE Main 2022 (Online) 25th June Morning Shift

Given below are two statements :

Statement I : Davisson-Germer experiment establishes the wave nature of electrons.

Statement II : If electrons have wave nature, they can interfere and show diffraction.

In the light of the above statements choose the correct answer from the option given below :

A.
Both Statement I and Statement II are true.
B.
Both Statement I and Statement II are false.
C.
Statement I is true but Statement II is false.
D.
Statement I is false but Statement II is true.
2022 JEE Mains MCQ
JEE Main 2022 (Online) 24th June Evening Shift

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :

A.
1 : 1
B.
2 : 1
C.
4 : 1
D.
1 : 4
2022 JEE Mains Numerical
JEE Main 2022 (Online) 26th June Evening Shift

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 $\mathop A\limits^o $ is 0.42 V. If the threshold frequency is x $\times$ 1013 /s, where x is _________ (nearest integer).

(Given, speed light = 3 $\times$ 108 m/s, Planck's constant = 6.63 $\times$ 10$-$34 Js)

2022 JEE Mains Numerical
JEE Main 2022 (Online) 24th June Morning Shift

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is v1. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v2. If v2 = x v1, the value of x will be __________.

2021 JEE Mains MCQ
JEE Main 2021 (Online) 1st September Evening Shift
The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is :

[me = mass of electron = 9 $\times$ 10$-$31 kg, h = Planck constant = 6.6 $\times$ 6.6 $\times$ 10$-$34 Js, kB = Boltzmann constant = 1.38 $\times$ 10$-$23 JK$-$1]
A.
6.26 nm
B.
8.46 nm
C.
2.26 nm
D.
3.25 nm
2021 JEE Mains MCQ
JEE Main 2021 (Online) 31st August Evening Shift
A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $\times$ 10$-$34 Js)
A.
1.45 $\times$ 1016 MHz
B.
0.19 $\times$ 1015 MHz
C.
1.45 $\times$ 109 MHz
D.
9.0 $\times$ 1027 MHz
2021 JEE Mains MCQ
JEE Main 2021 (Online) 31st August Evening Shift
Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-
A.
${\left( {{{{m_p}} \over {{m_e}}}} \right)^{3/2}}$
B.
$\sqrt {{{{m_e}} \over {{m_p}}}} $
C.
$\sqrt {{{{m_p}} \over {{m_e}}}} $
D.
${{{m_p}} \over {{m_e}}}$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 31st August Morning Shift
A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :
A.
Kp < Ke and Pp = Pe
B.
Kp = Ke and Pp = Pe
C.
Kp < Ke an Pp < Pe
D.
Kp > Ke and Pp = Pe
2021 JEE Mains MCQ
JEE Main 2021 (Online) 27th August Evening Shift
A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm?
A.
0.96 V
B.
1.25 V
C.
0.24 V
D.
1.5 V
2021 JEE Mains MCQ
JEE Main 2021 (Online) 27th August Morning Shift
In a photoelectric experiment, increasing the intensity of incident light :
A.
increases the number of photons incident and also increases the K.E. of the ejected electrons
B.
increases the frequency of photons incident and increases the K.E. of the ejected electrons
C.
increases the frequency of photons incident and the K.E. of the ejected electrons remains unchanged
D.
increases the number of photons incident and the K.E. of the ejected electrons remains unchanged
2021 JEE Mains MCQ
JEE Main 2021 (Online) 26th August Evening Shift
The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?
A.
${1 \over 9}$E
B.
${7 \over 9}$E
C.
E
D.
${16 \over 9}$E
2021 JEE Mains MCQ
JEE Main 2021 (Online) 26th August Morning Shift
In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $\phi$ = 2.5 eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential. (h = 6.63 $\times$ 10$-$34 Js, c = 3 $\times$ 108 ms$-$1)
A.
1.3 V
B.
1.1 V
C.
1.9 V
D.
0.6 V
2021 JEE Mains MCQ
JEE Main 2021 (Online) 27th July Evening Shift
An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$\mathop A\limits^o $. What is the maximum kinetic energy of the emitted photoelectron?
A.
7.61 eV
B.
1.41 eV
C.
3.3 eV
D.
No photoelectron would be emitted
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th July Evening Shift
An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :
A.
${{3c} \over v}$
B.
${v \over {3c}}$
C.
${v \over {2c}}$
D.
${{2c} \over v}$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th July Evening Shift
When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is :
A.
2$\lambda$
B.
4$\lambda$
C.
8$\lambda$
D.
6$\lambda$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th July Morning Shift
What should be the order of arrangement of de-Broglie wavelength of electron ($\lambda$e), an $\alpha$-particle ($\lambda$a) and proton ($\lambda$p) given that all have the same kinetic energy?
A.
$\lambda$e = $\lambda$p = $\lambda$$\alpha$
B.
$\lambda$e < $\lambda$p < $\lambda$$\alpha$
C.
$\lambda$e > $\lambda$p > $\lambda$$\alpha$
D.
$\lambda$e = $\lambda$p > $\lambda$$\alpha$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th July Morning Shift
A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :
A.
1 : 3
B.
3 : 1
C.
1 : $\sqrt 3 $
D.
1 : 1
2021 JEE Mains MCQ
JEE Main 2021 (Online) 22th July Evening Shift
An electron of mass me and a proton of mass mp are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is
A.
${{{m_e}} \over {{m_p}}}$
B.
1
C.
${{{m_p}} \over {{m_e}}}$
D.
$\sqrt {{{{m_p}} \over {{m_e}}}} $
2021 JEE Mains MCQ
JEE Main 2021 (Online) 20th July Evening Shift
An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is :
A.
0
B.
${{2{m^2}{c^2}{\lambda ^2}} \over {{h^2}}}$
C.
${{2mc{\lambda ^2}} \over h}$
D.
${{hc} \over {mc}}$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 20th July Morning Shift
The radiation corresponding to 3 $\to$ 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 $\times$ 10$-$4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is : (Mass of electron = 9.1 $\times$ 10$-$31 kg)
A.
1.36 eV
B.
1.88 eV
C.
0.82 eV
D.
0.16 eV
2021 JEE Mains MCQ
JEE Main 2021 (Online) 18th March Evening Shift
The speed of electrons in a scanning electron microscope is 1 $\times$ 107 ms-1. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :
A.
${1 \over {1837}}$
B.
1837
C.
${\sqrt {1837} }$
D.
${1 \over {\sqrt {1837} }}$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 18th March Morning Shift
A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :
A.
${1 \over {16}}$ times the mass of e$-$
B.
8 times the mass of e$-$
C.
16 times the mass of e$-$
D.
${1 \over {8}}$ times the mass of e$-$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 17th March Evening Shift
Two identical photocathodes receive the light of frequencies f1 and f2 respectively. If the velocities of the photo-electrons coming out are v1 and v2 respectively, then
A.
${v_1} - {v_2} = {\left[ {{{2h} \over m}({f_1} - {f_2})} \right]^{{1 \over 2}}}$
B.
$v_1^2 + v_2^2 = {{2h} \over m}[{f_1} + {f_2}]$
C.
${v_1} + {v_2} = {\left[ {{{2h} \over m}({f_1} + {f_2})} \right]^{{1 \over 2}}}$
D.
$v_1^2 - v_2^2 = {{2h} \over m}[{f_1} - {f_2}]$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 17th March Morning Shift
An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)
A.
${1 \over c}{\left( {{{2m} \over E}} \right)^{1/2}}$
B.
${1 \over c}{\left( {{E \over {2m}}} \right)^{1/2}}$
C.
${\left( {{E \over {2m}}} \right)^{1/2}}$
D.
$c{(2mE)^{1/2}}$
2021 JEE Mains MCQ
JEE Main 2021 (Online) 16th March Evening Shift
The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? (mp = 1.00727u me = 0.00055u)
A.
41.4 : 1
B.
(1860)2 : 1
C.
1860 : 1
D.
43 : 1
2021 JEE Mains MCQ
JEE Main 2021 (Online) 16th March Morning Shift
The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation :
A.
Phase
B.
Frequency
C.
Amnplitude
D.
Intensity
2021 JEE Mains MCQ
JEE Main 2021 (Online) 26th February Evening Shift
The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :
A.
4.34 m/s
B.
2.19 m/s
C.
3.25 m/s
D.
4.17 m/s
2021 JEE Mains MCQ
JEE Main 2021 (Online) 26th February Morning Shift
Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R.

Assertion A : An electron microscope can achieve better resolving power than an optical microscope.

Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.

In the light of the above statements, choose the correct answer from the options given below :
A.
A is false but R is true.
B.
Both A and R are true but R is NOT the correct explanation of A.
C.
Both A and R are true and R is the correct explanation of A.
D.
A is true but R is false.
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th February Evening Shift
An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength ${{{}^\lambda electron} \over {{}^\lambda proton}}$ will be :
A.
1
B.
1836
C.
${1 \over {1836}}$
D.
918
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th February Evening Shift
The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :
A.
400 nm
B.
329 nm
C.
309 nm
D.
382 nm
2021 JEE Mains MCQ
JEE Main 2021 (Online) 25th February Morning Shift
An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $\lambda$$\alpha$ and $\lambda$p respectively. The ratio ${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$ is :
A.
8
B.
2.8
C.
7.8
D.
3.8
2021 JEE Mains MCQ
JEE Main 2021 (Online) 24th February Evening Shift
An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :
A.
10$-$2 nm
B.
10$-$1 nm
C.
10$-$3 nm
D.
10$-$4 nm
2021 JEE Mains MCQ
JEE Main 2021 (Online) 24th February Evening Shift
The de-Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :
A.
4 : 2
B.
4 : 3
C.
4 : 1
D.
1 : 4
2021 JEE Mains MCQ
JEE Main 2021 (Online) 24th February Morning Shift
Given below are two statements :

Statement I : Two photons having equal linear momenta have equal wavelengths.

Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.

In the light of the above statements, choose the correct answer from the options given below.
A.
Statement I is false but Statement II is true
B.
Both Statement I and Statement II are false
C.
Both Statement I and Statement II are true
D.
Statement I is true but Statement II is false
2021 JEE Mains Numerical
JEE Main 2021 (Online) 27th July Morning Shift
A particle of mass 9.1 $\times$ 10$-$31 kg travels in a medium with a speed of 106 m/s and a photon of a radiation of linear momentum 10$-$27 kg m/s travels in vacuum. The wavelength of photon is __________ times the wavelength of the particle.
2021 JEE Mains Numerical
JEE Main 2021 (Online) 25th July Evening Shift
A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular are of radius 30 cm. The value of B is ___________ $\times$ 10$-$7 T.

Given hc = 20 $\times$ 10$-$26 J-m, mass of electron = 9 $\times$ 10$-$31 kg
2021 JEE Mains Numerical
JEE Main 2021 (Online) 20th July Evening Shift
A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is 3V0. If the same surface is illuminated with a radiation of wavelength 2$\lambda$, the stopping potential is V0. The threshold wavelength of this surface for photoelectric effect is ____________ $\lambda$.
2021 JEE Mains Numerical
JEE Main 2021 (Online) 26th February Evening Shift
Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ___________.
2020 JEE Mains MCQ
JEE Main 2020 (Online) 6th September Evening Slot
Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to :
(Given : nitrogen molecule weight : 4.64 $ \times $ 10–26 kg,
Boltzman constant: 1.38 $ \times $ 10–23 J/K,
Planck constant : 6.63 $ \times $ 10–34 J.s)
A.
0.44 $\mathop A\limits^o $
B.
0.34 $\mathop A\limits^o $
C.
0.20 $\mathop A\limits^o $
D.
0.24 $\mathop A\limits^o $
2020 JEE Mains MCQ
JEE Main 2020 (Online) 6th September Morning Slot
An electron, a doubly ionized helium ion (He++) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $\lambda $e, $\lambda $He++ and $\lambda $p is :
A.
$\lambda $e > $\lambda $He++ > $\lambda $p
B.
$\lambda $e < $\lambda $p < $\lambda $He++
C.
$\lambda $e > $\lambda $p > $\lambda $He++
D.
$\lambda $e < $\lambda $He++ = $\lambda $p
2020 JEE Mains MCQ
JEE Main 2020 (Online) 4th September Evening Slot
In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased : JEE Main 2020 (Online) 4th September Evening Slot Physics - Dual Nature of Radiation Question 148 English
A.
Slope of the straight line get more steep
B.
Graph does not change
C.
Straight line shifts to left
D.
Straight line shifts to right
2020 JEE Mains MCQ
JEE Main 2020 (Online) 4th September Morning Slot
Given figure shows few data points in a phot electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is:
(Plancks constant h = 6.62 × 10–34 J.s) JEE Main 2020 (Online) 4th September Morning Slot Physics - Dual Nature of Radiation Question 149 English
A.
2.10 eV
B.
2.27 eV
C.
2.59 eV
D.
1.93 eV
2020 JEE Mains MCQ
JEE Main 2020 (Online) 4th September Morning Slot
Particle A of mass mA = ${m \over 2}$ moving along the x-axis with velocity v0 collides elastically with another particle B at rest having mass mB = ${m \over 3}$. If both particles move along the x-axis after the collision, the change $\Delta $$\lambda $ in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength ($\lambda $0) before collision is :
A.
$\Delta $$\lambda $ = ${5 \over 2}{\lambda _0}$
B.
$\Delta $$\lambda $ = ${3 \over 2}{\lambda _0}$
C.
$\Delta $$\lambda $ = 2$\lambda $0
D.
$\Delta $$\lambda $ = 4$\lambda $0
2020 JEE Mains MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
A.
${1 \over {500}}$
B.
500
C.
250
D.
${1 \over {250}}$
2020 JEE Mains MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :
A.
1.02 eV
B.
0.81 eV
C.
0.61 eV
D.
0.52 eV