Advertisements
Advertisements
प्रश्न
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.
उत्तर
Data: mp = 1836 me
(a) The de Broglie wavelength, λ = `"h"/"p" = "h"/"mv"`
`lambda_"e"/lambda_"p" = ("m"_"p"/"m"_"e")("v"_"p"/"v"_"e")` = 1836 as vp = ve
Thus, λe < λp.
(b) λ = `"h"/"p" = "h"/sqrt"2mK"`, where K denotes the kinetic energy `(1/2 "mv"^2)`
∴ `lambda_"e"/lambda_"p" = sqrt(("m"_"p" "K"_"p")/("m"_"e""K"_"e")) = sqrt("m"_"p"/"m"_"e") = sqrt1836 = 42.85`
as Kp = Ke
Thus, λe > λp.
(c) λ = `"h"/"p"`
∴ `lambda_"e"/lambda_"p" = "p"_"p"/"p"_"e" = 1` as pp = pe.
APPEARS IN
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 ______.
State the importance of Davisson and Germer experiment.
What is the speed of a proton having de Broglie wavelength of 0.08 Å?
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?
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.
Explain De Broglie’s Hypothesis.
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 ______
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) ______.
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 ____________.
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) ____________.
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?
If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?
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] ____________.
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)
An electron is accelerated through a potential difference of 100 volts. Calculate de-Broglie wavelength in nm.
