Advertisements
Advertisements
Question
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.
Options
b and d
a and c
b, c and d
a, c and d
Advertisements
Solution
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
RELATED QUESTIONS
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?
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
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.
Compute the typical de Broglie wavelength of an electron in a metal at 27°C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10−10 m.
Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.
Which one of the following deflect in electric field
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 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 ______.
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 A with a mass m A is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.
An electron is accelerated from rest through a potential difference of 100 V. Find:
- the wavelength associated with
- the momentum and
- the velocity required by the electron.
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to ______.
The graph which shows the variation of `(1/lambda^2)` and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle):
Which relation gives the de Broglie wavelength of a particle of mass \[m\] moving with speed \[v\]?
In the de Broglie relation, what does \[h\] represent?
In de Broglie's proposal, a moving material particle of total energy \[E\] and momentum \[p\] has a wave associated with it analogous to what?
Which phenomenon does the concept of matter waves help explain?
What value of Planck's constant is used in the de Broglie wavelength calculations?
