S. L. Arora Solutions for Chapter: Dual Nature of Radiation and Matter, Exercise 2: Problems For Practice

What is the de Broglie wavelength associated with (Take, the mass of the electron as, $m = 9.1\times {10}^{-31} \mathrm{kg}, h = 6.6\times {10}^{-34} \mathrm{Js}$)
(i) an electron moving with a speed of $5.4\times {10}^{6 }{\mathrm{ms}}^{-1}$ and
(ii) a ball of mass $1.50 \mathrm{g}$ travelling at $30.0 \mathrm{m}/\mathrm{s}?$

An electron is accelerated through a potential difference of $64 \mathrm{V}$. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond. Mass of the electron, $m = 9.1\times {10}^{-31} \mathrm{kg}$

What potential difference must be applied to an electron microscope to produce an electron beam of wavelength $0.41 {\mathrm{A}}^0$?

Calculate the de Broglie wavelength of an electron of kinetic energy $100 \mathrm{eV}$. Given $m=9.1\times {10}^{-31} \mathrm{kg}$, $e=1.6\times {10}^{-19} \mathrm{C},$ and $h=6.62\times {10}^{-34} \mathrm{Js}.$

For what kinetic energy of a proton, will the associated de Broglie wavelength be $16.5 \mathrm{nm}$? Mass of proton $m_p=1.675\times {10}^{-27} \mathrm{kg}, h=6.63\times {10}^{-34} \mathrm{Js}$.

An electron is revolving around the nucleus with a constant speed of $2.5\times {10}^8 \mathrm{m}/\mathrm{s}.$ Find the de-Broglie wavelength associated with it. Take, $h = 6.6\times {10}^{-34 }\mathrm{Js}$, mass of the electron, $m = 9.1\times {10}^{-31} \mathrm{kg}$

An electron and a photon each have a wavelength $2 \mathrm{nm}$. Find

(i) their momenta,

(ii) the energy of the photon and

(iii) the kinetic energy of electron.
$h = 6.6\times {10}^{-34} \mathrm{Js}$