Advertisements
Advertisements
प्रश्न
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
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which
(a) an electron, and
(b) a neutron, would have the same de Broglie wavelength.
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).
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E = hv, p = `"h"/lambda`
But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?
A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.
State any one phenomenon in which moving particles exhibit wave nature.
Which one of the following deflect in electric field
The de-Broglie wavelength associated with a material particle when it is accelerated through a potential difference of 150 volt is 1 Å. What will be the de-broglie wavelength associated with the same particle when it is accelerated through a potential difference of 4500 V?
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 (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 ______.
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.
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
How does the de Broglie wavelength depend on momentum?
Which phenomenon does the concept of matter waves help explain?
