Advertisements
Advertisements
Question
Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn= 1.675 × 10−27 kg)
Advertisements
Solution
De Broglie wavelength = 2.327 × 10−12 m; neutron is not suitable for the diffraction experiment.
Kinetic energy of the neutron, K = 150 eV
= 150 × 1.6 × 10−19
= 2.4 × 10−17 J
Mass of a neutron, mn = 1.675 × 10−27 kg
The kinetic energy of the neutron is given by the relation:
`"K" = 1/2 "m"_"n""v"^2`
`"m"_"n""v" = sqrt(2 "KM"_"n")`
Where
v = Velocity of the neutron
mnv = Momentum of the neutron
De-Broglie wavelength of the neutron is given as:
`lambda = "h"/("m"_"n""v") = "h"/(sqrt(2 "Km"_"n"))`
it is clear that wavelength is inversely proportional to the square rot of mass.
Hence wavelength decrease with an increase in mass and vice versa.
∴ `lambda = (6.6 xx 10^(-34))/sqrt(2 xx 2.4 xx 10^(-17) xx 1.675 xx 10^(-27))`
= 2.327 × 10−12 m
It is given in the previous problem that the inter-atomic spacing of a crystal is about 1 Å, i.e., 10−10 m. Hence, the inter-atomic spacing is about a hundred times greater. Hence, a neutron beam of energy 150 eV is not suitable for diffraction experiments.
RELATED QUESTIONS
What is the de Broglie wavelength of a dust particle of mass 1.0 × 10−9 kg drifting with a speed of 2.2 m/s?
An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
Compute the typical de Broglie wavelength of an electron in a metal at 27°C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10−10 m.
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.
What are matter waves?
Show with the help of a labelled graph how their wavelength (λ) varies with their linear momentum (p).
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).
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?
- λ = 10 nm
- λ = 10–1 nm
- λ = 10–4 nm
- λ = 10–6 nm
A proton and an α-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths λp and λa related to each other?
Given below are two statements:
Statement - I: Two photons having equal linear momenta have equal wavelengths.
Statement - II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the correct answer from the options given below.
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 ______.
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
