Advertisements
Advertisements
Question
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
Advertisements
Solution
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
RELATED QUESTIONS
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
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
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.
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.
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.
Show with the help of a labelled graph how their wavelength (λ) varies with their linear momentum (p).
Which one of the following deflect in electric field
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).
How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.
Matter waves are ______.
What are matter waves?
Which relation gives the de Broglie wavelength of a particle of mass \[m\] moving with speed \[v\]?
Which wave quantities did de Broglie relate to the particle quantities energy and momentum?
Why did de Broglie propose an associated wavelength for a moving particle?
Which phenomenon does the concept of matter waves help explain?
