An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vacuum)
For electron
De - Broglie wavelength $$\lambda_c = \dfrac{h}{p}$$
where p is momentum $$p = mv$$
also by energy we have $$E = \dfrac{1}{2} mv^2$$
$$\Rightarrow E = \dfrac{1}{2} \dfrac{p^2}{m}$$
$$\Rightarrow p = \sqrt{2 mE}$$
$$\therefore \lambda_c = \dfrac{h}{\sqrt{2 mE}}$$
For photon energy $$\Rightarrow E = \dfrac{hc}{\lambda}$$
$$\Rightarrow \lambda = \dfrac{h c}{E}$$
$$\therefore \dfrac{\lambda_c}{\lambda} = \dfrac{h}{\sqrt{2 mE}} \dfrac{E}{hc}$$
$$= \dfrac{1}{C} \sqrt{\dfrac{E}{2m}}$$
option (A) is correct.
An electron (mass $$m$$) with initial velocity $$\vec { v } ={ v }_{ 0 }\hat { i } +{ v }_{ 0 }\hat { j } $$ is an electric field $$\vec { E } =-{ E }_{ 0 }\hat { k } $$. If $${ \lambda }_{ 0 }$$ is initial de-Broglie wave length at time $$t$$ is given by
An electron of mass $$m$$ and magnitude of charge $$|e|$$ initially at rest gets accelerated by a constant electric field $$E$$. The rate of change of de-Broglie wavelength of this electron at time $$t$$ ignoring relativistic effects is:
If the deBroglie wavelenght of an electron is equal to $$10^{3}$$ times the wavelength of a photon of frequency $$6 \times 10^{14} Hz$$, then the speed of electron is equal to : (Speed of light = $$3 \times 10^8 m/s$$ Planck's constant = $$6.63 \times 10^{34} J$$ . Mass of electron = $$9.1 10^{31} kg$$)
The de - Broglie wavelength associated with the electron in the $$n=4$$ level is :
If electron charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental constant h are taken as fundamental quantities, the permeability of vacuum $$\mu_0$$ can be expressed in units of
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $$4.65 \mathring{A}$$). The de-Broglie wavelength of this electron is:
Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are $${ \lambda }_{ 1 }$$ and $${ \lambda }_{ 2 }$$, their de Broglie wavelength in the frame of reference attached to their centre of mass is:
The de-Broglie wavelength $$(\lambda_{B})$$ associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state $$(\lambda_{G})$$ by :
A particle $$A$$ of mass $$m$$ and initial velocity $$v$$ collides with a particle $$B$$ of mass $$\dfrac{m}{2}$$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $${\lambda}_A$$ to $${\lambda}_B$$ after the collision is :