Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
remains constant.
increases with time.
decreases with time.
increases and decreases periodically.
Advertisements
उत्तर
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 remains constant.
Explanation:
If a particle is carrying a positive charge q and moving with a velocity v and enters a magnetic field 5 then it experiences a force F which is given by the expression
F = q(v × B) = $ F = qvB sin θ. As this force is perpendicular to v and B, so the magnitude of v will not change, i.e. momentum (p = mv) will remain constant in magnitude.
According to the problem, `vecv = v_0i` and `vecB = B_0j`
Magnetic force on moving electron = `-e[v_0i xx B_0j] ⇒ - ev_0B_0k`
As this force is perpendicular to `vecv` and `vecB`, so the magnitude of v will not change, i.e. momentum (p = mv) will remain constant in magnitude. Hence, de-Broglie wavelength `lambda = h/(mv)` remains constant.
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?
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 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)
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.
When a light wave travels from air to glass ______.
What are matter waves?
Show with the help of a labelled graph how their wavelength (λ) varies with their linear momentum (p).
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).
Which one of the following deflect in electric field
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
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 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.
An electron of mass me, and a proton of mass mp = 1836 me are moving with the same speed. The ratio of the de Broglie wavelength `lambda_"electron"/lambda_"proton"` will be:
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
