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प्रश्न
Explain De Broglie’s Hypothesis.
उत्तर
- De Broglie proposed that a moving material particle of total energy E and momentum p has a wave associated with it (analogous to a photon).
- He suggested a relation between properties of the wave, like frequency and wavelength, with that of a particle, like energy and momentum.
p = `"E"/"c" = "hv"/"c" = "h"/lambda` - Thus, the frequency and wavelength of a wave associated with a material particle, of mass m moving with a velocity v, are given as
`"v" = "E"/"h"` and `lambda = "h"/"p" = "h"/"mv"` ….(1) - De Broglie referred to these waves associated with material particles as matter waves. The wavelength of the matter waves, given by equation (1), is now known as de Broglie wavelength and the equation is known as de Broglie relation.
संबंधित प्रश्न
An electron, a proton, an α-particle, and a hydrogen atom are moving with the same kinetic energy. The associated de Broglie wavelength will be longest for ______.
Explain what you understand by the de Broglie wavelength of an electron. Will an electron at rest have an associated de Broglie wavelength? Justify your answer.
The de Broglie wavelengths associated with an electron and a proton are the same. What will be the ratio of (i) their momenta (ii) their kinetic energies?
Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an α-particle, what are the possibilities for the other particle?
Find the ratio of the de Broglie wavelengths of an electron and a proton when both are moving with the (a) same speed, (b) the same kinetic energy, and (c) the same momentum. State which of the two will have a longer wavelength in each case.
According to De-Broglie, the waves are associated with ______
An electron is accelerated through a potential of 120 V. Find its de Broglie wavelength.
Calculate De Broglie's wavelength of the bullet moving with speed 90m/sec and having a mass of 5 gm.
The momentum of a photon of energy 1 MeV in kg m/s will be ______
The de Broglie wavelength associated with photon is, ____________.
According to de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is 'λe'· Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is 'λp'. If the energy (E) of electron and photon is same then relation between 'λe' and 'λp' is ______.
An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is ( c being velocity of light) ______.
What is the momentum of a photon having frequency 1.5 x 1013 Hz?
A particle of charge q, mass m and energy E has de-Broglie wavelength `lambda.` For a particle of charge 2q, mass 2m and energy 2E, the de-Broglie wavelength is ____________.
How much energy is imparted to an electron so that its de-Broglie wavelength reduces from 10-10 m to 0.5 × 10-10 m? (E =energy of electron)
If '`lambda_1`' and '`lambda_2`' are de-Broglie wavelengths for electrons in first and second Bohr orbits in hydrogen atom, then the ratio '`lambda_2`' to '`lambda_1`' is (E1 = -13.6 eV) ____________.
If the kinetic energy of a particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is ____________.
Graph shows the variation of de-Broglie wavelength `(lambda)` versus `1/sqrt"V"`, where 'V' is the accelerating potential for four particles carrying same charge but of masses m1 , m2, m3, m4. Which particle has a smaller mass?
According to de-Broglie hypothesis, the ratio of wavelength of an electron and that of photon having same energy 'E' is (m = mass of electron, c = velocity of light) ____________.
A photon of wavelength 3315 Å falls on a photocathode and an electron of energy 3 x 10-19 J is ejected. The threshold wavelength of photon is [Planck's constant (h) = 6.63 x 10-34 J.s, velocity of light (c) = 3 x 108 m/s] ____________.
Explain de-Broglie wavelength.
Obtain an expression for de-Broglie wavelength of wave associated with material particles. The photoelectric work function for metal is 4.2 eV. Find the threshold wavelength.
A proton, a neutron, an electron and an α-particle have same energy. λp, λn, λe and λα are the de Broglie's wavelengths of proton, neutron, electron and α particle respectively, then choose the correct relation from the following :
The energy of an electron having de-Broglie wavelength `λ` is ______.
(h = Plank's constant, m = mass of electron)
An electron of mass m has de-Broglie wavelength λ when accelerated through potential difference V. When proton of mass M, is accelerated through potential difference 9V, the de-Broglie wavelength associated with it will be ______. (Assume that wavelength is determined at low voltage)
