Advertisements
Advertisements
प्रश्न
An alpha particle is accelerated through a potential difference of 100 V. Calculate:
- The speed acquired by the alpha particle, and
- The de-Broglie wavelength is associated with it.
(Take mass of alpha particle = 6.4 × 10−27 kg)
Advertisements
उत्तर
(i) `1/2 "mv"^2` = qV
or, `1/2"mv"^2` = 2e × 100
or, mv2 = 400 eV
or, v = `sqrt((400 "eV")/"m")`
or, v = `sqrt((400 xx 1.6 xx 10^-19)/(6.4 xx 10^-27))`
∴ v = 105 m/s
(ii) de-Broglie wavelength = λ = `"h"/sqrt(2"mqV")`
or, λ = `(6.6 xx 10^-34)/(sqrt(2 xx 6.4 xx 10^-27 xx 2 xx 1.6 xx 10^-19 xx 100))`
∴ λ = 1.03 × 10−12 m
APPEARS IN
संबंधित प्रश्न
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
Calculate the momentum of the electrons accelerated through a potential difference of 56 V.
Calculate the de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
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.
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.
The wavelength λ of a photon and the de-Broglie wavelength of an electron have the same value. Show that energy of a photon in (2λmc/h) times the kinetic energy of electron; where m, c and h have their usual meaning.
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 ______.
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).
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.
