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
Calculate the de Broglie wavelength 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.
Find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of `(3/2)` kT at 300 K.
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).
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.
State any one phenomenon in which moving particles exhibit wave nature.
Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons.
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
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).
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
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).
Two particles move at a right angle to each other. Their de-Broglie wavelengths are λ1 and λ2 respectively. The particles suffer a perfectly inelastic collision. The de-Broglie wavelength λ, of the final particle, is given by ______.
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?
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
