Advertisements
Advertisements
प्रश्न
Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 Å, which is of the order of inter-atomic spacing in the lattice) (me = 9.11 × 10−31 kg).
Advertisements
उत्तर
An X-ray probe has greater energy than an electron probe for the same wavelength.
Wavelength of light emitted from the probe, λ = 1 Å = 10−10 m
Mass of an electron, me = 9.11 × 10−31 kg
Planck’s constant, h = 6.6 × 10−34 Js
Charge on an electron, e = 1.6 × 10−19 C
The kinetic energy of the electron is given as:
`"E" = 1/2 "m"_"e""v"^2`
`"m"_"e""v" = sqrt(2"Em"_"e")`
Where,
v = Velocity of the electron
mev = Momentum (p) of the electron
According to the de Broglie principle, the de Broglie wavelength is given as:
`lambda = "h"/"p" = "h"/("m"_"e""v") = "h"/sqrt(2"Em"_"e")`
∴ E = `"h"^2/(2lambda^2"m"_"e")`
`= (6.6 xx 10^(-34))^2/(2xx(10^(-10))^2 xx 9.11 xx 10^(-31))`
= 2.39 × 10−17 J
= `(2.39 xx 10^(-17))/(1.6 xx 10^(-19))`
= 149.375 eV
Energy of a photon `"E'" = "hc"/(lambda"e") "eV"`
= `(6.6 xx 10^(-34) xx 3 xx 10^8) /(10^(-10) xx 1.6 xx 10^(-19))`
= 12.375 × 103 eV
= 12.375 keV
Hence, a photon has greater energy than an electron for the same wavelength.
APPEARS IN
संबंधित प्रश्न
Calculate the momentum of the electrons accelerated through a potential difference of 56 V.
What is the
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
State any one phenomenon in which moving particles exhibit wave nature.
The wavelength λ of a photon and the de-Broglie wavelength of an electron have the same value. Show that energy of a photon in (2λmc/h) times the kinetic energy of electron; where m, c and h have their usual meaning.
Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the gas through the same range at constant volume will be (assume R = 2 cal/mol-K).
Which one of the following deflect in electric field
An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λd, then ______
An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength ______.
An electron (mass m) with an initial velocity `v = v_0hati` is in an electric field `E = E_0hatj`. If λ0 = h/mv0, it’s de Broglie wavelength at time t is given by ______.
A particle A with a mass m A is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.
Two particles move at a right angle to each other. Their de-Broglie wavelengths are λ1 and λ2 respectively. The particles suffer a perfectly inelastic collision. The de-Broglie wavelength λ, of the final particle, is given by ______.
The De-Broglie wavelength of electron in the third Bohr orbit of hydrogen is ______ × 10-11 m (given radius of first Bohr orbit is 5.3 × 10-11 m):
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to ______.
Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?
How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.
