Dual Nature of Radiation and Matter

A monochromatic source of light operating at 15 kW emits 2.5 1022 photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to . (Take h=6.6 10-34 J.s and c=3 108 m/s).

1. Microwave
2. Infrared
3. Visible
4. Ultraviolet

K1 and K2 be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength 1 and 2, respectively. If 1=2 2 then the work function of material is given by :

1. K2+2K1
2. 2K2-K1
3. K1-2K2
4. K2-2K1

An electron of mass m is moving in an electric field E=-2E0 i (E0 = constant > 0), with an initial velocity V=v0 i (v0 = constant > 0). If 0= h4mv0, its de Broglie wavelength at time t is . (e = charge of electron)

1. 4 0 [1- E0e2m tv0 ]
2. 4 0 [1+ E0e2m tv0 ]
3. 4 0 [1+ 2E0em tv0 ]
4. 4 0 [1- 2E0em tv0 ]

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is 10-19 J. The value of is . (h=6.62 10-34 J s, e=1.6 10-19 C and c=3 108 m/s)

1. 3.68
2. 4.68
3. 5.68
4. 2.68

An electron is travelling with a velocity v in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is 0, where 0 is its de Broglie wavelength in free space. The value of is .

1. 1.20
2. 1.0
3. 1.25
4. 0.75

The graph shows variation of stopping potential V0 with the frequency of the incident radiation for three photosensitive metals X1, X2 and X3. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [figure]

1. X1
2. X2
3. X3
4. All the metals will give out photoelectrons with same kinetic energies.

The de Broglie wavelength associated with an electron accelerated through a potential difference V is e and the de Broglie wavelength associated with a proton accelerated through the same potential difference is p. If their corresponding masses are me and mp, respectively, then the ratio of their de Broglie wavelengths ( e p ) is .

1. mpme
2. memp
3. mpme
4. ( mpme )2

For a certain metal, when monochromatic light of wavelength is incident, the stopping potential for photoelectrons is 3V0. When the same metal is illuminated by light of wavelength 2 , then the stopping potential becomes V0. The threshold wavelength for photoelectric emission for the given metal is . The value of is .

1. 1
2. 4
3. 2
4. 3

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is . (Given : h = 6.63 10-34 J s and c = 3 108 m/s)

1. 10 1015
2. 5 1016
3. 5 1015
4. 2 1016

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V. The wavelength of first light is m. (h = 6.63 10-34 J s, e = 1.6 10-19 C, c = 3 108 m/s)

1. 2.9 10-8
2. 2.5 10-7
3. 3.1 10-7
4. 2.2 10-8

The de Broglie wavelength of an oxygen molecule at 27 is x 10-12 m. The value of x is (take Planck's constant = 6.63 10-34 J s, Boltzmann constant = 1.38 10-23 J/K, mass of oxygen molecule = 5.31 10-26 kg)

1. 24
2. 30
3. 20
4. 26

Light is incident on a metallic plate having work function 110 10-20 J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is rad/s. (h = 6.63 10-34 J s)

1. 1.04 1013
2. 1.66 1016
3. 1.66 1015
4. 1.04 1016

A light wave described by E = 60 [ (3 1015 t ) + (12 1015 t ) ] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately) eV. (h = 6.6 10-34 J s and e = 1.6 10-19 C)

1. 3.8
2. 7.8
3. 6.0
4. 5.1

A photoemissive substance is illuminated with a radiation of wavelength i so that it releases electrons with de-Broglie wavelength e. The longest wavelength of radiation that can emit photoelectron is o. Expression for de-Broglie wavelength is given by: (m: mass of the electron, h: Planck's constant and c: speed of light)

1. e = h i 2mc
2. e = h 2mc ( 1 i - 1 o )
3. e = h2mc ( 1 i - 1 o )
4. e = h o2mc

A small mirror of mass m is suspended by a massless thread of length l. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity)

1. = Emc gl
2. = E2mc gl
3. = 3E4mc gl
4. = 2Emc gl

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the correct answer from the options given below

1. Both A and R are true and R is the correct explanation of A
2. A is false but R is true
3. Both A and R are true but R is NOT the correct explanation of A
4. A is true but R is false

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is

1. Red
2. Green
3. Blue
4. Yellow

If and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass, the correct graphical representation for the particle will be :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is false but (R) is true
4. (A) is true but (R) is false

In an experiment with photoelectric effect, the stopping potential,

1. is ( 1e ) times the maximum kinetic energy of the emitted photoelectrons
2. increases with increase in the intensity of the incident light
3. decreases with increase in the intensity of the incident light
4. increases with increase in the wavelength of the incident light

A proton of mass 'mp' has same energy 'E' as that of a photon of wavelength ' '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is

1. 1c Emp
2. 1c 2Emp
3. 12c Emp
4. 1c E2mp

Which of the following phenomena cannot be explained by wave theory of light?

1. Refraction of light
2. Reflection of light
3. Diffraction of light
4. Compton effect

An electron of mass 'm' with an initial velocity v=v0 i (v0>0) enters an electric field E=-Eo k. If the initial de Broglie wavelength is 0, the value after time t would be

1. o 1- e2Eo2t2m2vo2
2. 0
3. o 1+ e2Eo2t2m2vo2
4. o 1+ e2Eo2t2m2vo2

In photoelectric effect, the stopping potential (V0) v/s frequency ( ) curve is plotted. ( h is the Planck's constant and 0 is work function of metal ) Choose the correct answer from the options given below :

1. (A), (C) and (E) only
2. (C) and (D) only
3. (A), (B) and (C) only
4. (D) and (E) only

A sub-atomic particle of mass 10-30 kg is moving with a velocity 2.21 106 m/s. Under the matter wave consideration, the particle will behave closely like (h=6.63 10-34 J.s )

1. X-rays
2. Infra-red radiation
3. Gamma rays
4. Visible radiation

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V, what is the wavelength of the em-wave? (Given hc=1242 eV nm where h is the Planck's constant and c is the speed of light in vacuum.)

1. 400 nm
2. 600 nm
3. 300 nm
4. 200 nm

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

1. Both Cs and Li
2. Neither Cs nor Li
3. Li only
4. Cs only

A light source of wavelength illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength 2, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

1. 5 eV
2. 3 eV
3. 2 eV
4. 6 eV

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

1. p > e >
2. < p < e
3. e > > p
4. p < e <

UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be:

1. 4.13 eV
2. 1 eV
3. 7.26 eV
4. 3.13 eV