Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 2: Level 2

A particle $\mathrm{A}$ of mass $m$ and initial velocity $v$ collides with a particle $\mathrm{B}$ of mass $\frac{m}{2}$ which is at rest. The $\frac{m}{2}$ collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\mathrm{\lambda }}_{\mathrm{A}} \mathrm{to} {\mathrm{\lambda }}_{\mathrm{B}}$ after the collision is :

Electrons with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-ray is:

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is

The surface of a metal is illuminated with a light of wavelength $400 \mathrm{nm}$. The kinetic energy of the ejected photoelectrons was found to be $1.68 \mathrm{eV}$. The work function of the metal is $\left(hc=1240 \mathrm{eV} \mathrm{nm}\right)$,

The maximum energy of electrons released in a photocell is independent of

If the wavelength of light is $4000 \mathrm{\AA },$ then the number of waves in $1 \mathrm{mm}$ length will be

The wavelength $\lambda$ of de Broglie waves associated with an electron (mass $m$, charge $e$) accelerated through a potential difference of $V$ is given by ($h$ is Planck’s constant) :