Advertisements
Advertisements
Question
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
Options
`H`
`H^(1/2)`
`H^0`
`H^(-1/2)`
Advertisements
Solution
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to `underline(H^(-1/2))`.
Explanation:
According to de-Broglie a moving material particle sometimes acts as a wave and sometimes as a particle.
The wave associated with a moving particle is called matter wave or de-Broglie wave and it propagates in the form of wave packets with the group velocity. According to de-Broglie theory, the wavelength of de-Broglie wave is given by `H = v = sqrt(2gH)`
We know that de-Broglie wavelength `λ = h/p`
`λ = h/(mv) = h/(msqrt(2gH)`
h, m and g are constant
∴ `h/(msqrt(2g)` is constant ⇒ `λ oo 1/sqrt(H)` ⇒ `λ oo H^(-1/2)`
APPEARS IN
RELATED QUESTIONS
Describe the construction of photoelectric cell.
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
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).
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)
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
The wavelength of the matter wave is dependent on ______.
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 ______.
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.
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
Which phenomena support the wave model of light?
Which phenomena support the particle model of light?
What are matter waves?
Which relation gives the de Broglie wavelength of a particle of mass \[m\] moving with speed \[v\]?
In the de Broglie relation, what does \[\lambda\] represent?
In the de Broglie relation, what does \[p\] represent?
In \[\lambda=\frac{h}{mv}\], what do \[m\] and \[v\] represent, respectively?
Rearranging \[p=\frac{h}{\lambda}\] gives which expression?
What de Broglie wavelength is obtained for the electron?
