Dual nature of radiation and matter practice · Medium

A photodiode sensor is used to measure the output of a $300 {~W}$ lamp kept $10 {~m}$ away. The sensor has an opening of $2 {~cm}$ in diameter. How many photons enter the sensor if the wavelength of the light is $660 {~nm}$ and the exposure time is $100 {~ms}$. (Assume that all the energy of the lamp is given off as light and $\left.h=6.6 \times 10^{-34} {Js}\right)$

The wave nature of electrons was first experimentally verified independently by

Which of the following transitions in a hydrogen atom emits photon of the highest frequency

The energy that should be added to an electron, to reduce its de-Broglie wavelength from ${10^{ - 10}}m$ to $0.5 \times {10^{ - 10}}m,$ will be

Given below are two statements:
Statement I: Davisson-Germer experiment establishes the wave nature of electrons.
Statement II: If electrons have wave nature, they can interfere and show diffraction.
In the light of the above statements choose the correct answer from the option given below:

The work function for caesium is $1.8 \mathrm{~eV}$. Light of $5000 ~\mathop {\text{A}}\limits^ \circ$ is incident on it. Calculate maximum kinetic energy of the emitted electrons. Given : $h=6.6 \times 10^{-34} \mathrm{~Js}$, $m_e=9 \times 10^{-31} \mathrm{~kg}, c=3 \times 10^8 \mathrm{~ms}^{-1}$.

The constant $A$ in the Richardson-Dushman equation for tungsten is $60 \times 10^4 \mathrm{~A} \mathrm{~m}^{-2} \mathrm{~K}^{-2}$. The work function of tungsten is $4.5 \mathrm{~eV}$. A tungsten cathode having a surface area $2.0 \times 10^{-5} \mathrm{~m}^2$ is heated by a $24 \mathrm{~W}$ electric heater. In steady state, the heat radiated by the cathode equals the energy input by the heater and the temperature becomes constant. Assuming that the cathode radiates like a blackbody, calculate the saturation current due to thermions. Take Stefan constant $=6 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$. Assume that the thermions take only a small fraction of the heat supplied.

Find the maximum magnitude of the linear momentum of a photoelectron emitted when light of wavelength $400 \mathrm{~nm}$ falls on a metal having work function $2.5 \mathrm{~eV}$.

From the photoelectric effect experiment, following observations are made. Identify which of these are correct.
A. The stopping potential depends only on the work function of the metal.
B. The saturation current increases as the intensity of incident light increases.
C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light.
D. Photoelectric effect can be explained using wave theory of light.

Choose the correct answer from the options given below:

A particle with rest mass ${m_0}$ is moving with speed of light $c$. The de-Broglie wavelength associated with it will be

In Millikans oil drop experiment, a charged drop of mass $1.8 \times {10^{ - 14}}kg$ is stationary between its plates. The distance between its plates is $0.90\;cm$ and potential difference is $2.0\;kilo\;volts.$ The number of electrons on the drop is

In photoelectric experiment graph of stopping potential versus $\frac{1}{\text {Wavelength}}$ is drawn. Nature and reciprocal of slope of graph will be

Assertion: Photo electric current increases if the distance between cathode and anode is increased.

Reason: Momentum of photon is directly proportional to its wavelength.

A monochromatic source, emitting light of wavelength, $600 \mathrm{~nm}$, has a power output of $66 \mathrm{~W}$. Calculate the number of photons emitted by this source in 2 minutes.

The potential energy of a particle of mass $m$ is given by

$U\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {{E_0};\;0 \le x \le 1}\\ {0;\;\;\;\;\;\;\;x > 1} \end{array}} \right.$

${\lambda _1}$ and ${\lambda _2}$ are the de-Broglie wavelengths of the particle, when $0 \le x \le 1$ and $x > 1$ respectively. If the total energy of particle is $2{E_0},$ the ratio $\frac{{{\lambda _1}}}{{{\lambda _2}}}$ will be

Assertion: Work function of a metal is $8 \mathrm{eV}$. Two photons each having energy 5 $\mathrm{eV}$ can't eject the electron from the metal.

Reason: More than one photon can't collide simultaneously with an electron.

Electric field and magnetic field in a region of space is given by $\mathbf{E}=E_0 \hat{\mathbf{j}}$ and $\mathbf{B}=B_0 \hat{\mathbf{j}}$. A particle of specific charge $\alpha$ is released from origin with velocity $\mathbf{v}=v_0 \hat{\mathbf{i}}$. Then, path of particle

Assertion: de-Broglie wavelength of an electron accelerated through a potential difference of ${V}$ volt is $\lambda=\frac{12.72}{\sqrt{V}}{A}$

Reason: de-Broglie wavelength of an electron is given by $\lambda=\frac{h}{m v}$.

A beam of $450 \mathrm{~nm}$ light is incident on a metal having work function $2.0 \mathrm{~eV}$ and placed in a magnetic field $B$. The most energetic electrons emitted perpendicular to the field are bent in circular arcs of radius $20 \mathrm{~cm}$. Find the value of $B$.

Which of the following cannot be explained on the basis of photoelectric theory?

I. Instantaneous emission of photoelectrons

II. Existence of threshold frequency

III. Sufficiently intense beam of radiation can emit photoelectrons

IV. Existence of stopping potential

Assertion: Speed of light is independent of frame of reference.

Reason: Speed of light is the ultimate speed of particle.

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal vs the frequency of the incident radiation gives a straight line whose slope

The linear momentum of a photon corresponding to wavelength of radiation $\lambda$ is

The minimum intensity of light to be detected by human eye is ${10^{ - 10}}W/{m^2}.$ The number of photons of wavelength $5.6 \times {10^{ - 7}}m$ entering the eye, with pupil area ${10^{ - 6}}{m^2},$ per second for vision will be nearly

A proton and an $\mathrm{\alpha }$-particle are accelerated through the same potential difference. The ratio of their de-Broglie wavelength $\left( {{\lambda _p}/{\lambda _\alpha }} \right)$ is

The material used for making thermionic cathode must have

Calculate the threshold frequency of photon for photoelectric emission from a metal of work function $0.1 \mathrm{~eV}$.

A moving proton and electron have the same de-Broglie wavelength. If $k\,\mathrm{and}\,p$ denote the KE and momentum, respectively. Then, choose the correct option.

If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same

The linear momentum of photon is $p$. The wavelength of photon is $\lambda \;,$ then ($h$ is Planck constant)