Advertisements
Advertisements
प्रश्न
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.
पर्याय
b and d
a and c
b, c and d
a, c and d
Advertisements
उत्तर
b and d
Explanation:
According to the question, here given that the de-Broglie wavelength of the particle can be varying cyclically between two values λ1 and λ2, it is possible if particle is moving in an elliptical orbit with origin as its one focus.
As shown in the figure given alongside,
Let v1 and v2 be the speed of particle at A and B respectively and origin is at focus O. If λ1 and λ2 are the de-Broglie wavelengths associated with particle while moving at A and B respectively, then `λ_1 = h/(mv_1)`
And `λ_2 = h/(mv_2)`
∴ `λ_1/λ_2 = v_2/v_1`
Since `λ_1 > λ_2`
∴ `v_2 > v_1`
By the law of conservation of angular momentum, the particle moves faster when it is closer to focus.
From figure, we note that origin O is closed to P than A.
APPEARS IN
संबंधित प्रश्न
Describe the construction of photoelectric cell.
Calculate the momentum of the electrons accelerated through a potential difference of 56 V.
What is the de Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 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.
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).
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.
What are matter waves?
The wavelength of the matter wave is dependent on ______.
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
Assuming an electron is confined to a 1 nm wide region, find the uncertainty in momentum using Heisenberg Uncertainty principle (∆x∆p ≃ h). You can assume the uncertainty in position ∆x as 1 nm. Assuming p ≃ ∆p, find the energy of the electron in electron volts.
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).
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)
The equation λ = `1.227/"x"` nm can be used to find the de Brogli wavelength of an electron. In this equation x stands for:
Where,
m = mass of electron
P = momentum of electron
K = Kinetic energy of electron
V = Accelerating potential in volts for electron
A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be:
Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?
Matter waves are ______.
