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
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.
What is the de Broglie wavelength of a bullet of mass 0.040 kg travelling at the speed of 1.0 km/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 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)
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.
Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons.
What are matter waves?
The wavelength of the matter wave is dependent on ______.
A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λp to that λα is _______.
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 ______.
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
An electron (mass m) with an initial velocity `v = v_0hati (v_0 > 0)` is in an electric field `E = - E_0hati `(E0 = constant > 0). It’s de Broglie wavelength at time t is given by ______.
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 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.
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?
An alpha particle is accelerated through a potential difference of 100 V. Calculate:
- The speed acquired by the alpha particle, and
- The de-Broglie wavelength is associated with it.
(Take mass of alpha particle = 6.4 × 10−27 kg)
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
Matter waves are ______.
