Advertisements
Advertisements
प्रश्न
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
उत्तर
`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
संबंधित प्रश्न
Describe the construction of photoelectric cell.
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
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?
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
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?
A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
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 ______.
An electron (mass m) with an initial velocity `v = v_0hati` is in an electric field `E = E_0hatj`. If λ0 = h/mv0, it’s de Broglie wavelength at time t is given by ______.
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.
The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is `v_e = c/100`. Then ______.
- `E_e/E_p = 10^-4`
- `E_e/E_p = 10^-2`
- `p_e/(m_ec) = 10^-2`
- `p_e/(m_ec) = 10^-4`
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).
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):
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
