Dual Nature of Radiation and Matter

The de Broglie wavelength for an electron accelerated through the potential difference of V1 volt is 1. When the potential difference is changed to V2 volt, the associated de Broglie wavelength is increased by 50%. If (V1/V2 )= (9/ ), then the value of is .

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 ]

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 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

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)

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

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 .

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

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]

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