Advertisements
Advertisements
Question
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.
Advertisements
Solution
`m_Av = m_Av_1 + m_Bv_2`
`1/2 m_Av^2 = 1/2 m_Av_1^2 + 1/2 m_Bv_2^2`
∴ `1/2 m_A(v - v_1)(v_A + v_1) = 1/2 m_Bv_B^2`
∴ `v + v_1 = v_2`
or `v = v_2 - v_1`
∴ `v_1 = ((m_A - m_B)/(m_A + m_B))v` and `v_2 = ((2m_A)/(m_A + m_B))v`
∴ `λ_"initial" = h/(m_Av)`
`λ_"final" = h/(m_Av) = |(h(m_A + m_B))/(m_A(m_A - m_B)v)|`
∴ Δλ = `h/(m_Av) [|(m_A + m_B)/(m_A - m_B)| - 1]`
APPEARS IN
RELATED QUESTIONS
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
Calculate the de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
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 wavelength of the matter wave is dependent on ______.
An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λd, then ______.
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
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 A1 sand A2 of masses m1, m2 (m1 > m2) have the same de Broglie wavelength. Then ______.
- their momenta are the same.
- their energies are the same.
- energy of A1 is less than the energy of A2.
- energy of A1 is more than the energy of A2.
Assuming an electron is confined to a 1 nm wide region, find the uncertainty in momentum using Heisenberg Uncertainty principle (∆x∆p ≃ h). You can assume the uncertainty in position ∆x as 1 nm. Assuming p ≃ ∆p, find the energy of the electron in electron volts.
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).
Given below are two statements:
Statement - I: Two photons having equal linear momenta have equal wavelengths.
Statement - II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the correct answer from the options given below.
The De-Broglie wavelength of electron in the third Bohr orbit of hydrogen is ______ × 10-11 m (given radius of first Bohr orbit is 5.3 × 10-11 m):
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:
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 ______.
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
