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प्रश्न
Explain De Broglie’s Hypothesis.
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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
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
- their momenta
- their kinetic energies?
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.
An electron is accelerated through a potential of 120 V. Find its de Broglie wavelength.
The momentum of a photon of energy 1 MeV in kg m/s will be ______
The de Broglie wavelength associated with photon is, ____________.
If the radius of the innermost Bohr orbit is 0.53 Å, the radius of the 4th orbit is ______
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 ____________.
If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?
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) ____________.
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.
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)
An electron is accelerated through a potential difference of 100 volts. Calculate de-Broglie wavelength in nm.
Calculate the de Broglie wavelength associated with an electron moving with a speed of `5 xx 10^6` m/s. `(m_e = 9.1 xx 10^(-31)kg)`
