Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 3: Exercise - 3

During the propagation of electromagnetic waves in a medium

The allowed energy for the particle for a particular value of $n$ is proportional to length of string $a$ as:

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons $N=4\times {10}^{27} {\mathrm{m}}^{–3}$. Take ${\mathrm{\epsilon }}_0={10}^{–11}$ and $m={10}^{–30}$, where these quantities are in proper SI units.

A pulse of light of duration $100 \mathrm{ns}$ is absorbed completely by a small object initially at rest. Power of the pulse is $30 \mathrm{mW}$ and the speed of light is $3\times {10}^8 {\mathrm{ms}}^{–1}$. The final momentum of the object is :

Match$\mathrm{List}-\mathrm{I}$(Fundamental Experiment) with $\mathrm{List}-\mathrm{II}$ (its conclusion) and select the correct option from the choices given in the options

Radiation of wavelength $\mathrm{\lambda }$, is incident on a photocell. The fastest emitted electron has speed $\text{'}v\text{'}$. If the wavelength is changed to $\frac{3\mathrm{\lambda }}{4}$ , the speed of the fastest emitted electron will be :

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $\mathrm{X}\text{-rays.}$ It produces continuous as well as characteristic $\mathrm{X}\text{-rays.}$ If${\mathrm{\lambda }}_{\min }$is the smallest possible wavelength of  $\mathrm{X}\text{-ray}$ in the spectrum, the variation of $\log \left({\lambda }_{\min }\right)$ with $\log \left(V\right)$ is correctly represented in:

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 :