Dual Nature of Radiation and Matter PYQs

Match List I with List II. Choose the correct answer from the options given below.Match List I with List II. Choose the correct answer from the options given below.

For a metal of work function 6.6 eV, which of the following wavelengths of incident radiation does not give rise to the photoelectric effect? (Take Planck's constant as 6.6 × 10⁻³⁴ J s)

A bulb is rated at 150 watt, converting 8% energy into light. If energy of one photon is 4.42 × 10⁻¹⁹ J, how many photons are emitted by the bulb per second?

De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm)

A photon and an electron (mass $m$) have the same energy $E$. The ratio $\left(\lambda_{\text{photon}}/\lambda_{\text{electron}}\right)$ of their de Broglie wavelengths is: ($c$ is the speed of light)

Which of the following options represent the variation of photoelectric current with property of light shown on the x-axis?

If c is the velocity of light in free space, the correct statements about photon among the following are: A. The energy of a photon is E = hν. B. The velocity of a photon is c. C. The momentum of a photon, p = (hv/c). D. In a photon-electron collision, both total energy and total momentum are conserved. E. Photon possesses positive charge.

The graph which shows the variation of (1/λ²) and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle):

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to:

The work functions of Caesium (Cs), Potassium (K) and Sodium (Na) are 2.14 eV, 2.30 eV and 2.75 eV respectively. If incident electromagnetic radiation has an incident energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?

When two monochromatic lights of frequency $\nu$ and $\frac{\nu}{2}$ are incident on a photoelectric metal, their stopping potentials become $\frac{V_s}{2}$ and $V_s$ respectively. The threshold frequency for this metal is:

The graph which shows the variation of the de Broglie wavelength (λ) of a particle and its associated momentum (p) is

The number of photons per second on an average emitted by the source of monochromatic light of wavelength $600\ \text{nm}$, when it delivers the power of $3.3 \times 10^{-3}\ \text{W}$ will be ($h = 6.6 \times 10^{-34}\ \text{J s}$)

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If a photoelectron of mass $m$ emitted from the surface has de-Broglie wavelength $\lambda_d$, then:

Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled?

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 × 10⁻² nm, the potential difference is:

The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photoemission from the substance is approximately:

A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λₚ and $λ_α$ are in the ratio:

An electron of mass m with an initial velocity $\vec{V} = V_0\hat{i}$ ($V_0 > 0$) enters an electric field $\vec{E} = -E_0\hat{i}$ ($E_0$ = constant > 0) at t = 0. If $\lambda_0$ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is:

When the light of frequency $2\nu_0$ (where $\nu_0$ is the threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is $v_1$. When the frequency of the incident radiation is increased to $5\nu_0$, the maximum velocity of electrons emitted from the same plate is $v_2$. The ratio of $v_1$ to $v_2$ is:

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ Kelvin and mass $m$, is

The photoelectric threshold wavelength of silver is $3250 \times 10^{-10}\,\text{m}$. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength $2536 \times 10^{-10}\,\text{m}$ is: (Given: $h = 4.14 \times 10^{-15}\,\text{eV s}$ and $c = 3 \times 10^8\,\text{m/s}$)

Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cutoff wavelength $(\lambda_0)$ of the emitted X-rays is:

Photons with energy $5\ \text{eV}$ are incident on a cathode $C$ in a photoelectric cell. The maximum kinetic energy of emitted photoelectrons is $2\ \text{eV}$. When photons of energy $6\ \text{eV}$ are incident on $C$, no photoelectrons will reach anode $A$, if the stopping potential of $A$ relative to $C$ is:

Light of wavelength $500\,\text{nm}$ is incident on a metal with work function $2.28\,\text{eV}$. The de Broglie wavelength of the emitted electron is:

A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\dfrac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface material is: ($h$ = Planck's constant, $c$ = speed of light)

Light with an energy flux of 25 × 10⁴ W m⁻² falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm², the average force exerted on the surface is:

When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increases from 0.5 eV to 0.8 eV. The work function of the metal is:

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is:

Calculate the energy in joule corresponding to light of wavelength 45 nm. (Planck's constant h = 6.63 × 10⁻³⁴ Js; speed of light c = 3 × 10⁸ ms⁻¹)

For photoelectric emission from a certain metal the cut-off frequency is $\nu$. If radiation of frequency $2\nu$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be (where $m$ is electron mass)

The wavelength $\lambda_e$ of an electron and $\lambda_p$ of a photon of same energy $E$ are related by

A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?

The value of Planck’s constant is $6.63\times10^{-34}\,Js$. The speed of light is $3\times10^{17}\,nm\,s^{-1}$. Which value is closest to the wavelength in nanometre of a quantum of light with frequency $6\times10^{15}\,s^{-1}$?

Two radiations of photon energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is:

If the momentum of an electron is changed by P, then the de Broglie wavelength associated with it changes by 0.5%. The initial momentum of electrons will be:

The threshold frequency for a photosensitive metal is 3.3 × 10¹⁴ Hz. If light of frequency 8.2 × 10¹⁴ Hz is incident on this metal, the cut-off voltage for the photoelectric emission is nearly:

An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, the value of n is:

When monochromatic radiation of intensity I falls on a metal surface, the number of photoelectrons and their maximum kinetic energy are N and T respectively. If the intensity of radiation becomes 2I, the number of emitted electrons and their maximum kinetic energy are respectively

A 0.66 kg ball is moving with a speed of 100 m/s. The associated wavelength will be: (h = 6.6 × 10⁻³⁴ Js)

The number of photoelectrons emitted for light of frequency $\nu$ (higher than threshold frequency $\nu_0$) is proportional to:

Monochromatic light of wavelength $667\,\mathrm{nm}$ is produced by a helium-neon laser. The power emitted is $9\,\mathrm{mW}$. The number of photons arriving per second on the average at a target irradiated by this beam is:

The figure shows a plot of photo current versus anode potential for a photosensitive surface for three different radiations. Which one of the following is correct?

The work function of a surface of a photosensitive material is 6.2 eV. The wavelength of the incident radiation for which the stopping potential is 5 V lies in the

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 × 10⁶ ms⁻¹. The velocity of the particle is (mass of electron = 9.1 × 10⁻³¹ kg)

If uncertainty in position and momentum are equal, then uncertainty in velocity is

The measurement of the electron position is associated with an uncertainty in momentum, which is equal to 1 × 10⁻¹⁸ g cm s⁻¹. The uncertainty in electron velocity is, (mass of an electron is 9 × 10⁻²⁸ g)

How many photons of wavelength 439 nm should strike on a perfectly reflecting surface in 1 second so that it may exert a force of 10 N?

In photoelectric effect, a photon of wavelength 3300 Å is incident on a metal surface of work function 2.5 eV. The emitted electrons enter a transverse magnetic field of 6.7 × 10⁻⁶ T and move in a circular path of radius 50 cm. Calculate the charge of the electron from the given data.

A photo-cell employs photoelectric effect to convert:

When photons of energy hν fall on an aluminium plate (of work function E₀), photoelectrons of maximum kinetic energy K are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be:

The momentum of a photon of energy 1 MeV in kg m/s will be:

The work functions for metals $A$, $B$ and $C$ are respectively $1.92\,\mathrm{eV}$, $2.0\,\mathrm{eV}$ and $5\,\mathrm{eV}$. According to Einstein's equation, the metals which will emit photoelectrons for a radiation of wavelength $4100\,\text{\AA}$ are:

A photosensitive metallic surface has work function $h\nu_0$. If photons of energy $2h\nu_0$ fall on this surface, the electrons come out with a maximum velocity of $4 \times 10^6\ \mathrm{m\,s^{-1}}$. When the photon energy is increased to $5h\nu_0$, then the maximum velocity of photoelectrons will be: