Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 1: JEE Advanced Paper 1 - 2015

In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals $P,Q$ and $R$ are $E_P, E_Q$ and $E_R$, respectively, and they are related by $E_P=2E_Q=2E_R$. In this experiment, the same source of monochromatic light is used for metals $P$ and $Q$ while a different source of monochromatic light is used for the metal $R$. The work functions for metals $P,Q$ and $R$ are $4.0 \mathrm{eV}, 4.5 \mathrm{eV}$ and $5.5 \mathrm{eV}$, respectively. The energy of the incident photon used for metal $R$, in $eV$ is ___.

In a photoelectric experiment, a parallel beam of monochromatic light with the power of $200\text{W}$ is incident on a perfectly absorbing cathode of work function $6.25 \mathrm{eV}$. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of $500\text{V}$ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $F=n\times {10}^{-4}\mathrm{ N}$ due to the impact of the electrons. The value of $n$ is __________. Mass of the electron $m_e=9\times {10}^{-31}\mathrm{ kg} \mathrm{a}\mathrm{n}\mathrm{d} 1.0 \mathrm{eV}=1.6\times {10}^{-19}\mathrm{ J}$.

A photoelectric material having work-function ${\varphi }_0$ is illuminated with a light of wavelength $\lambda \left(\lambda <\frac{hc}{{\varphi }_0}\right)$. The fastest photoelectron has a de Broglie wavelength ${\lambda }_d$. A change in wavelength of the incident light by $\mathrm{\Delta }\lambda$ results in a change $\mathrm{\Delta }{\lambda }_d$ in ${\lambda }_d$. The ratio $\frac{\mathrm{\Delta }{\lambda }_d}{\mathrm{\Delta }\lambda }$ is proportional to

Light of wavelength ${\lambda }_{ph}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\varphi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is ${\lambda }_e,$ which of the following statement(s) is(are) true ?

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio $u_1:u_2=2:1$ and $hc=1240 \mathrm{eV} \mathrm{nm}$, the work function of the metal is nearly

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength $\left(\lambda \right)$ of incident light and the corresponding stopping potential $\left(V_0\right)$ are given below:
 

For photo-electric effect with incident photon wavelength $\mathrm{\lambda }$ , the stopping potential is ${\mathrm{V}}_0$ . Identify the correct variation(s) of ${\mathrm{V}}_0$ with $\mathrm{\lambda }$ and $\frac{1}{\mathrm{\lambda }}$ .

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 $3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$. The final momentum of the object is