Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 1: Exercise 1

A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the photoelectric surface is doubled, which of the following may result?

The electron in a hydrogen atom jumps back from an excited state to ground state, by emitting a photon of wavelength ${\lambda }_0=\frac{16}{15R},$ where $R$ is Rydberg's constant. In place of emitting one photon, the electron could come back to ground state by

The wavelength of an X-ray beam is $10 \mathrm{\AA }.$ The mass of a fictitious particle having the same energy as that of the $\mathrm{X}$ - ray photons is $\frac{\mathrm{x}}{3} \mathrm{h} \mathrm{kg}.$ The value of $x$ is ________.

The threshold frequency for a certain metal is $3.3\times {10}^{14} \mathrm{Hz}$. If light of frequency $8.2\times {10}^{14} \mathrm{Hz}$ is incident on the metal, then the cut-off voltage for the photoelectric emission is approximately is $n \mathrm{volt}$. The value of $n$ is

A photosensitive surface is irradiated with light of wavelength $\lambda$, the stopping potential is $V$. When the same surface is irradiated with the light of wavelength $2\lambda$, stopping potential is $\frac{V}{3}$. The ratio of threshold wavelength $\left({\lambda }_{\max }\right)$ and the $\lambda$ is $x:1$. Write the value of $x$.

In a photoelectric experimental setup ultraviolet light of wavelength $350 \mathrm{nm}$ is incident on emitter plate $\left(E\right)$. The work function of the emitter plate is $\varphi =2.2\mathrm{eV}.\mathrm{AB}$ is a uniform wire resistor having length $\mathrm{L}=100 \mathrm{cm}$. Resistance of the wire $\mathrm{AB}$ is $10\Omega$ and the emf of the battery is $\mathrm{V}=10$ volt. The sliding contact $\mathrm{J}$ can be moved along the wire $\mathrm{AB}$. When the sliding contact is placed at end $\mathrm{B}$ of the wire resistor the micro-ammeter shows a reading of $\mathrm{i}=6\mu \mathrm{A}$. Assume that photoelectric current is very small compared to the current through the cell. Find the reading of the ammeter (in $\mu \mathrm{A}$ ) when the slider is moved to end $\mathrm{A}$ of the wire.

A photo-sensitive plate $\left(\varphi =1.2eV\right)$ is placed at $200 cm$ from a point source of light of$\lambda =4.8\times {10}^{-7} m$ and a power output of $1.0 W$. The light falls nearly normally to the plate.The approximate number of photons reaching the plate per square metre per second is $n\times {10}^{16}$. Find $n$, assuming the photon efficiency of plate to be $0.05\%$.Use : Area of plate $=0.25{ m}^2$.

The ratio of the de Broglie wavelength of a particle to that of an electron is $1.813\times {10}^{-4}$. The mass of the particle, if it moves three times faster than the electron is $\mathrm{Y}\times {10}^{-29} \mathrm{kg}$. Then the value of $Y$ is: $\left({\mathrm{m}}_{\mathrm{e}}=9.1\times {10}^{-31}\mathrm{ }\mathrm{kg}\right)$ (Approximate the answer to nearest integer)