Dual Nature of Radiation and Matter

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

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n is . (Assume mass of proton = mass of neutron)

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 particle having electric charge 3 10-19 C and mass 6 10-27 kg is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave associated with the particle is 10-12 m. The value of is . (Take Planck's constant = 6.6 10-34 J s)

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '- '. The rate of change of de-Broglie wave length associated with the electron varies inversely as nth power of time. The numerical value of n is .