Advertisements
Advertisements
Question
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 ______.
Options
`λ/((1 + (eE_0)/m t/v_0))`
`λ_0 (1 + (eE_0t)/(mv_0))`
`λ_0`
`λ_0t`
Advertisements
Solution
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 `underline(λ/((1 + (eE_0)/m t/v_0)))`.
Explanation:
Initial de-Broglie wavelength `λ_0 = h/(mv_0)`
Force on electron = F = qE v F = (– e)(– E0i)
`ma = eE_0i`
`a = (eE_0)/m i`
Velocity of electron after time t is v = v0 + at
`v = v_0i + (eE_0)/m i * t`
`v = [v_0 + (eE_0t)/m]hati`
∴ New de-Broglie wavelength `λ = h/(mv)`
`λ = h/(m[v_0 + (eE_0t)/m]hati) = h/(mv_0 [1 + (eE_0t)/(mv_0)])`
`λ = λ_0/([1 + (eE_0t)/(mv_0)])` ......`[∵ h/(mv_0) = λ_0 "from equation" I]`
APPEARS IN
RELATED QUESTIONS
Calculate the momentum of the electrons accelerated through a potential difference of 56 V.
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 ball of mass 0.060 kg moving at a speed of 1.0 m/s?
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.
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E = hv, p = `"h"/lambda`
But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?
Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons.
The wavelength of the matter wave is dependent on ______.
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.
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
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?
What are matter waves?
Which relation gives the de Broglie wavelength of a particle with momentum \[p\]?
Which wave quantities did de Broglie relate to the particle quantities energy and momentum?
How does the de Broglie wavelength depend on momentum?
What value of Planck's constant is used in the de Broglie wavelength calculations?
