# UNIT VIII: Dual Nature of Radiation and Matter - Online Test

Q1. The wavelength λe of an electron and λp of a photon of same energy E are related by
Explaination / Solution:

de Broglie wavelength for an electron

λe= h / √(2mE) ;

λe 1/√E ;

λe2 1/E  ------------- (1)

For photon

λp= hc / E ;

λp 1/E  ------------- (2)

From equation (1) and (2), we have So,

λp λe2

Q2. In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the voltage is changed to 224 kV, then the de Broglie wavelength associated with the electrons would
Explaination / Solution:

deBroglie wavelength λ 1/√V

λ12 = √(V2/V1) = √(224/14) = √16 = 4

λ1 = 4λ2

λ2 = λ1/4

Q3. A particle of mass 3 × 10–6 g has the same wavelength as an electron moving with a velocity 6×106 m s−1 . The velocity of the particle is
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Q4. When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is V/4. The threshold wavelength for the metallic surface is
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Q5. If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the electrons are emitted. Then the wavelength of the emitted electron is (Take h = 6.6 × 10–34 Js)
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Q6. A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and λ/2. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function at the surface of material is
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Q7. In photoelectric emission, a radiation whose frequency is 4 times threshold frequency of a certain metal is incident on the metal. Then the maximum possible velocity of the emitted electron will be
Explaination / Solution:

From Enistein's equation

Q8. Two radiations with photon energies 0.9 eV and 3.3 eV respectively are falling on a metallic surface successively. If the work function of the metal is 0.6 eV, then the ratio of maximum speeds of emitted electrons will be
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Q9. A light source of wavelength 520 nm emits 1.04 × 1015 photons per second while the second source of 460 nm  produces 1.38 × 1015 photons per second. Then the ratio of power of second source  to that of first source is
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Q10. The mean wavelength of light from sun is taken to be 550 nm and its mean power is 3.8 × 1026W. The number of photons received by the human eye per second on the average from sunlight is of the order of
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