Advertisements
Advertisements
प्रश्न
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
उत्तर
De Broglie wavelength of the neutron, λ = 1.40 × 10−10 m
Mass of a neutron, mn = 1.66 × 10−27 kg
Planck’s constant, h = 6.6 × 10−34 Js
Kinetic energy (K) and velocity (v) are related as:
`"K" = 1/2 "m"_"n""v"^2` …......(1)
De Broglie wavelength (λ) and velocity (v) are related as:
`lambda = "h"/("m"_"n""v")` ........(2)
Using equation (2) in equation (1), we get:
`"K" = 1/2 ("m"_"n""h"^2)/(lambda^2 "m"_"n"^2) = "h"^2/(2lambda^2"m"_"n")`
= `(6.63 xx 10^(-34))^2/(2xx(1.40 xx 10^(-10))^2 xx 1.66 xx 10^(-27))`
= 6.75 × 10−21 J
= `(6.75 xx 10^-21)/(1.6 xx 10^-19)`
= 4.219 × 10−2 eV
Hence, the kinetic energy of the neutron is 6.75 × 10−21 J or 4.219 × 10−2 eV.
APPEARS IN
संबंधित प्रश्न
Describe the construction of photoelectric cell.
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
Calculate the de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
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.
Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27°C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.
Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27°C) and 1 atm pressure, and compare it with the mean separation between two atoms under these conditions.
Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.
When a light wave travels from air to glass
What are matter waves?
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).
The wavelength of the matter wave is dependent on ______.
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 ______.
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 particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values λ1, λ2 with λ1 > λ2. Which of the following statement are true?
- The particle could be moving in a circular orbit with origin as centre.
- The particle could be moving in an elliptic orbit with origin as its focus.
- When the de Broglie wavelength is λ1, the particle is nearer the origin than when its value is λ2.
- When the de Broglie wavelength is λ2, the particle is nearer the origin than when its value is λ1.
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):
The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : `sqrt2`. Then, the ratio of Vp to Vd will be ______.
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
