A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corresponding stopping potentials ($V_s$). The graph shows the varia...
CBSE CLASS 12 • PHYSICS • CHAPTER 11
Dual Nature of Radiation and Matter
183 distinct questions across 249 board paper set appearances (2022–2026).
Assertion (A) : On increasing the intensity of incident light of frequency $\nu (> \nu_0)$ on a photosensitive surface, the photocurrent increases.
Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency $\nu (> \nu_0)$ of incident light.
Assertion (A) : Photoelectric current depends upon the intensity of the incident radiation.
Reason (R) : Stopping potential is independent of the intensity of the incident radiation.
The kinetic energy of a charged particle is increased to four times of its initial value. The de Broglie wavelength associated with the particle will :
(A) increase by $100%$ of its initial value.
(B) increase by $50%$ of its initial value.
(C) decrease by $25%$ of its initial value.
(D) decrease by...
Assertion (A) : Photoelectric effect is a spontaneous phenomenon.
Reason (R) : According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.
Assertion (A) : Electron emission from surface of zinc occurs when yellow light is incident on it.
Reason (R) : Energy of a photon of yellow light is more than the work function of zinc.
When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of lig...
A graph between the frequency of incident radiation ($\nu$) and the corresponding stopping potential ($V_0$) for a metal is a straight line. Let $\alpha$ and $\beta$ be the value of the slope and the value of the intercept on the $V_0$-axis respectively. Then, according to Einstein's photoelectric e...
A beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?
(A) The blue beam has more number of photons than the red beam.
(B) The red beam has more number of photons than the blue beam.
(C) Wavelength of red light is lesser than wavelength of bl...
Assertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value.
Reason (R) : Each metal has a definite work function.
Explain the following observations using Einstein's photoelectric equation :
(a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value.
(b) It is the frequency, and not the intensity of the incident light which affect...
A hydrogen atom consists of an electron revolving in a circular orbit of radius $r$ with certain velocity $v$ around a proton located at the nucleus of the atom. The electrostatic force of attraction between the revolving electron and the proton provides the requisite centripetal force to keep it in...
Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is $h\nu$, where $\nu$ is the frequency of incident light and $h$ is Planck's constant. The number of photons in a bea...
The frequency of a photon of energy $1\cdot326\text{ eV}$ is :
(A) $1\cdot18 \times 10^{14}\text{ Hz}$
(B) $3\cdot20 \times 10^{14}\text{ Hz}$
(C) $4\cdot20 \times 10^{15}\text{ Hz}$
(D) $4\cdot80 \times 10^{15}\text{ Hz}$
Assertion (A) : The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage.
Reason (R) : The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelect...
When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency ($\nu_0$) for the surface, no photoelectron is emitted. For a photon of frequency $\nu$ ($\nu > \nu_0$), the kinetic energy of the emitted photoelectr...
(iii) When the wavelength of a photon is doubled, how many times its wave number and frequency become, respectively ?
(A) $2, \frac{1}{2}$
(B) $\frac{1}{2}, \frac{1}{2}$
(C) $\frac{1}{2}, 2$
(D) $2, 2$
(iv) The momentum of a photon is $5.0 \times 10^{-29} \text{ kg m/s}$. Ignoring relativistic effects (if any), the wavelength of the photon is
(A) $1.33 \text{ }\mu\text{m}$
(B) $3.3 \text{ }\mu\text{m}$
(C) $16.6 \text{ }\mu\text{m}$
(D) $13.3 \text{ }\mu\text{m}$
Assertion (A) : Photoelectric current increases with an increase in intensity of incident radiation, for a given frequency of incident radiation and the accelerating potential.
Reason (R) : Increase in the intensity of incident radiation results in an increase in the number of photoelectrons emitted...
(a) (i) What are matter waves ? A particle of mass m and charge q is accelerated from rest through a potential difference V. Obtain an expression for de Broglie wavelength associated with the particle.
(ii) Monochromatic light of frequency $5.0 \times 10^{14} \text{ Hz}$ is produced by a source of p...
Assertion (A): Photoelectric effect demonstrates the particle nature of light.
Reason (R): Photoelectric current is proportional to frequency of incident radiation.
The quantum nature of light explains the observations on photoelectric effect as -
(A) there is a minimum frequency of incident radiation below which no electrons are emitted.
(B) the maximum kinetic energy of photoelectrons depends only on the frequency of incident radiation.
(C) when the metal sur...
Assertion (A) : Electrons are ejected from the surface of zinc when it is irradiated by yellow light.
Reason (R) : Energy associated with a photon of yellow light is more than the work function of zinc.
(a) Draw the graph showing the variation of the number (N) of scattered alpha particles with scattering angle ($\theta$) in Geiger - Marsden experiment. Infer two conclusions from the graph. OR (b) Plot suitable graphs to show the variation of photoelectric current with the collector plate potential...
(a) A proton and an $\alpha$ particle are moving with the same speed. Which one of them has greater value of de Broglie wavelength associated with it? Justify your answer. (b) Lights of wavelengths 430 nm, 450 nm and 660 nm are incident on a metal surface whose threshold wavelength is 600 nm. In whi...
(II) For radiation of frequency $v > v_2$ incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
(A) greater for metal A because it has a smaller work function.
(B) greater for metal B because it has a larger work function.
(C) greater for metal B because it has high...
(IV) The threshold frequency for a metal surface is $\nu_0$. If the radiation of frequency $3\nu_0$ illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is $E_1$. If the frequency were increased to $6\nu_0$, the maximum KE of the photoelectrons becomes $E_2$. Then $\left(\frac{...
Radiation of wavelength $200\text{ nm}$ is incident on a photosensitive surface of work function $4\cdot2\text{ eV}$. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
(A) $3\cdot5\text{ eV}$
(B) $3\cdot0\text{ eV}$
(C) $2\cdot5\text{ eV}$
(D) $2\cdot0\text{ e...
(a) Explain how the dual aspect of matter is evident in the de Broglie relation.
(b) Radiation of wavelength $\lambda$ is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.
Photoemission of electrons occurs from a metal ($\phi_0 = 1\cdot96\text{ eV}$) when light of frequency $6\cdot4 \times 10^{14}\text{ Hz}$ is incident on it. Calculate :
(a) Energy of a photon in the incident light,
(b) The maximum kinetic energy of the emitted electrons, and
(c) The stopping potenti...
The saturation current for a given photosensitive material depends on :
(A) work function of the material
(B) wavelength of the incident radiation
(C) intensity of the incident radiation
(D) collector plate potential
The stopping potential of photoelectrons is found to be $0.40\text{ V}$ when light of wavelength $500\text{ nm}$ is incident on a surface. The work function of the surface is close to :
(A) $1.20\text{ eV}$
(B) $1.48\text{ eV}$
(C) $2.08\text{ eV}$
(D) $6.48\text{ eV}$
A photon of wavelength $500\text{ nm}$ is emitted when an electron makes a transition from one state to the other state in an atom. The change in the total energy of the electron and change in its kinetic energy in $\text{eV}$ as per Bohr's model, respectively will be :
(A) $2\cdot48, -2\cdot48$
(...
The threshold frequency for a given metal is $3.6 \times 10^{14}\text{ Hz}$. If monochromatic radiations of frequency $6.8 \times 10^{14}\text{ Hz}$ are incident on this metal, find the cut-off potential for the photoelectrons.
The momentum (in $\text{kg m/s}$) of a photon of frequency $6.0 \times 10^{14}\text{ Hz}$ is :
(A) $6.63 \times 10^{-25}$
(B) $1.326 \times 10^{-27}$
(C) $2.652 \times 10^{-26}$
(D) $3.978 \times 10^{-24}$
Two beams, A and B whose photon energies are $3.3~\text{eV}$ and $11.3~\text{eV}$ respectively, illuminate a metallic surface (work function $2.3~\text{eV}$) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is :
(A) 3
(B) 9
(C) $\frac{1}{3}$
(D) $\fra...
Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let $\lambda_{\text{n}}$ and $\lambda_{\text{p}}$ be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for $\frac{\lambda_{\text{n}}}{\lambda_{\text{p}}}$.
Assertion (A) : In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light.
Reason (R) : Photoelectric current depends on the wavelength of the incident light.
In photoelectric effect experiment, show the variation of (a) photocurrent with collector plate potential for a given surface for different intensities of incident radiation. Do the curves meet at any point ? If so, why ? (b) photocurrent with intensity of radiation incident on a surface keeping the...
The variation of the stopping potential ($V_0$) with the frequency ($\nu$) of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will be maximum for m...
(a) (i) Define the terms : 'impact parameter' and 'distance of closest approach' for an $\alpha$-particle in Geiger-Marsden scattering experiment. (ii) What will be the value of the impact parameter for scattering angle (I) $\theta = 0^{\circ}$ and (II) $\theta = 180^{\circ}$ ? OR (b) Photoelectric ...
In a photoelectric experiment, the emitter plate is irradiated with radiation of $200\text{ nm}$. The photocurrent becomes zero when the collector plate potential is $-0.80\text{ V}$. Calculate the work function (in $\text{eV}$) of the emitter.
Answer the following questions :
(I) From the graph, the work functions of A and B are ($h$ is Planck's constant and $e$ value of charge on an electron)
(A) $v_1$ and $v_2$
(B) $V_1$ and $V_2$
(C) $h v_1$ and $h v_2$
(D) $\frac{h v_1}{\text{e}}$ and $\frac{h v_2}{\text{e}}$
Find the ratio $\left$\frac{\lambda_{\text{a}}}{\lambda_{\text{p}}}\right$$ of de Broglie wavelength $\lambda_{\text{a}}$ associated with an alpha particle to de Broglie wavelength $\lambda_{\text{p}}$ associated with a proton if both are moving with the (a) same velocity (b) same kinetic energy.
From the graph, the work functions of A and B are ($h$ is Planck's constant and $e$ value of charge on an electron)
(A) $v_1$ and $v_2$
(B) $V_1$ and $V_2$
(C) $h v_1$ and $h v_2$
(D) $\frac{h v_1}{e}$ and $\frac{h v_2}{e}$
From the graph, the work functions of A and B are ($h$ is Planck's constant and $e$ value of charge on an electron)
(A) $\nu_1$ and $\nu_2$
(B) $V_1$ and $V_2$
(C) $h\nu_1$ and $h\nu_2$
(D) $\frac{h\nu_1}{e}$ and $\frac{h\nu_2}{e}$
For radiation of frequency $\nu > \nu_2$ incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
(A) greater for metal A because it has a smaller work function.
(B) greater for metal B because it has a larger work function.
(C) greater for metal B because it has higher...
The maximum kinetic energy of the electrons emitted from a photo sensitive surface depends on
(A) work function of the surface '$\phi_0$' only.
(B) frequency of the incident radiation '$\nu$' only.
(C) intensity of the incident radiation 'I' only.
(D) Both $\phi_0$ and $\nu$.
In Bohr model of hydrogen atom, the electron makes a transition from $n = 5$ to $n = 1$ state. As a result, a photon of wavelength $\lambda$ is emitted in the process. The wavelength of the photon emitted when an electron makes a transition from energy level $n = 5$ to $n = 2$ will be
(A) $\frac{8}{...
A photosensitive surface is illuminated by radiations of wavelength $\lambda_1, \lambda_2$ ($>\lambda_1$) and $\lambda_3$ one by one and photoemission is observed in each case. $\lambda_1, \lambda_2$ lies in UV range and $\lambda_3$ in visible range. If $V_1$, $V_2$ and $V_3$ are stopping potential ...
In Bohr model of hydrogen atom, an electron makes a transition from $n = 4$ state to $n = 1$ state and a photon of frequency $\nu$ is emitted. The frequency of photon emitted when an electron makes a transition from $n = 4$ state to $n = 2$ state in the same model is
(A) $\frac{\nu}{3}$
(B) $\frac{\...
Calculate the de Broglie wavelength associated with an electron revolving in the second excited state of hydrogen atom. The ground state energy of the hydrogen atom is $-13.6\text{ eV}$. Take $m_e = 9 \times 10^{-31}\text{ kg}$, $h = 6.6 \times 10^{-34}\text{ J.s}$.
The equivalent mass of a photon of wavelength $100\text{ nm}$ is
(A) $2.21 \times 10^{-35}\text{ kg}$
(B) $6.63 \times 10^{-33}\text{ kg}$
(C) $1.11 \times 10^{-35}\text{ kg}$
(D) $3.31 \times 10^{-33}\text{ kg}$
The momentum of a photon of wavelength $663\text{ nm}$ is :
(A) $10^{-24}\text{ kg ms}^{-1}$
(B) $10^{-25}\text{ kg ms}^{-1}$
(C) $10^{-27}\text{ kg ms}^{-1}$
(D) $10^{-29}\text{ kg ms}^{-1}$
A beam of blue light is incident on a metal surface with a work function of $\phi_0 = \frac{hc}{550 \text{ nm}}$ and photoelectrons are ejected from the surface. If the blue light is replaced by red light of same intensity, then
(A) emitted electrons will be more energetic.
(B) emitted electrons wil...
Assertion (A) : Photoelectric effect demonstrates particle nature of light. Reason (R) : The number of photoelectrons emitted from a surface depends upon the intensity of radiation.
What is meant by threshold frequency ($\nu_0$) for photoelectric emission ? Does it depends on the intensity of light ? How does photoelectric current vary with the intensities of radiation of frequency $\nu (> \nu_0)$ ?
A proton and an alpha particle have equal momentum. The ratio of their kinetic energies $(E_p/E_a)$ and de Broglie wavelengths associated with them $(\lambda_p/\lambda_a)$ respectively are :
(A) $2, 1$
(B) $1, 2$
(C) $4, 1$
(D) $1, 4$
A particle of mass M at rest splits up into two particles of masses $m_1$ and $m_2$ having non-zero velocities. Calculate the ratio of the de Broglie wavelengths associated with the two particles.
The velocity of the photoelectrons emitted from a surface depends upon the :
(A) Wavelength of incident radiation only
(B) Intensity of incident radiation only
(C) Work function of the surface only
(D) Both wavelength of the incident radiation and work function of the surface
Calculate the de Broglie wavelength of a neutron having kinetic energy of 150 eV.
The ratio of the de Broglie wavelengths associated with the electron revolving in the first and third orbits in hydrogen atom is :
(A) 2
(B) $\frac{1}{2}$
(C) 3
(D) $\frac{1}{3}$
Radiation of wavelength $200 ext{ nm}$ is incident on a photosensitive surface of work function $4.2 ext{ eV}$. The kinetic energy of fastest photoelectrons emitted from this surface will be close to :
(A) $3.5 ext{ eV}$
(B) $3.0 ext{ eV}$
(C) $2.5 ext{ eV}$
(D) $2.0 ext{ eV}$
Light of frequency $5\cdot 0 \times 10^{14} \text{ Hz}$ is incident on a metal surface. If the maximum speed of photoelectrons emitted is $6\cdot 63 \times 10^{5} \text{ ms}^{-1}$, calculate the threshold frequency for the surface.
Radiation of wavelength $331 \text{ nm}$ irradiates the following metals :
| Metal | Work Function (eV) |
|---|---|
| Na | $1.92$ |
| K | $2.15$ |
| Ca | $3.20$ |
| Mo | $4.17$ |
Which of the following statements is correct ?
(A) Only Na and K show photoelectric emission.
(B) Only Mo will not show...
Radiation of wavelength $331 \text{ nm}$ irradiates the following metals :
| Metal | Work Function (eV) |
|---|---|
| Na | $1\cdot92$ |
| K | $2\cdot15$ |
| Ca | $3\cdot20$ |
| Mo | $4\cdot17$ |
Which of the following statements is correct ?
(A) Only Na and K show photoelectric emission.
(B) Only ...
Radiation of wavelength $331\text{ nm}$ irradiates the following metals :
| Metal | Work Function ($ ext{eV}$) |
|---|---|
| Na | $1\cdot92$ |
| K | $2\cdot15$ |
| Ca | $3\cdot20$ |
| Mo | $4\cdot17$ |
Which of the following statements is correct ?
(A) Only $ ext{Na}$ and $ ext{K}$ show photoelect...
Explain how the dual aspect of matter is evident in the de Broglie relation.
Radiation of wavelength $\lambda$ is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.
Light of which of the following colours will have the maximum energy in a photon associated with it ?
(A) Red light
(B) Yellow light
(C) Green light
(D) Blue light
The momentum of a photon associated with a microwave of wavelength $4\cdot00\text{ cm}$ is :
(A) $1\cdot66 \times 10^{-32}\text{ kg ms}^{-1}$
(B) $1\cdot83 \times 10^{-34}\text{ kg ms}^{-1}$
(C) $2\cdot05 \times 10^{-34}\text{ kg ms}^{-1}$
(D) $1\cdot66 \times 10^{-34}\text{ kg ms}^{-1}$
What are de Broglie waves? Show that the wavelength of the electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
A $500\text{ nm}$ photon is incident normally on a perfectly reflecting surface and is reflected. The value of momentum transferred to the surface is :
(A) $3.87 \times 10^{-43} \text{ kg ms}^{-1}$
(B) $2.5 \times 10^{-30} \text{ kg ms}^{-1}$
(C) $2.65 \times 10^{-27} \text{ kg ms}^{-1}$
(D) $1.33 \...
Photoemission of electrons occurs from a metal ($\phi_0 = 1.96\text{ eV}$) when light of frequency $6.4 \times 10^{14}\text{ Hz}$ is incident on it. Calculate :
(a) Energy of a photon in the incident light,
(b) The maximum kinetic energy of the emitted electrons, and
(c) The stopping potential.
The work function of a photosensitive surface is $2.21\text{ eV}$. The value of threshold frequency for the surface is :
(A) $4.8 \times 10^{14}\text{ Hz}$
(B) $5.3 \times 10^{14}\text{ Hz}$
(C) $1.9 \times 10^{15}\text{ Hz}$
(D) $1.2 \times 10^{15}\text{ Hz}$
Calculate the kinetic energy of an electron which has the de Broglie wavelength of $600\text{ nm}$ associated with it.
A photon of $3.8\text{ eV}$ energy is incident on a surface of work function $1.8\text{ eV}$. The maximum kinetic energy of the electron emitted from the surface will be :
(A) $3.2 \times 10^{-19}\text{ J}$
(B) $1.6 \times 10^{-19}\text{ J}$
(C) $1.25 \times 10^{-19}\text{ J}$
(D) $2.4 \times 10^{-1...
OR
The work function of a photosensitive surface is $2.21\text{ eV}$. The value of threshold frequency for the surface is :
(A) $4.8 \times 10^{14}\text{ Hz}$
(B) $5.3 \times 10^{14}\text{ Hz}$
(C) $1.9 \times 10^{15}\text{ Hz}$
(D) $1.2 \times 10^{15}\text{ Hz}$
A photon of $3\cdot8\text{ eV}$ energy is incident on a surface of work function $1\cdot8\text{ eV}$. The maximum kinetic energy of the electron emitted from the surface will be :
(A) $3\cdot2 \times 10^{-19}\text{ J}$
(B) $1\cdot6 \times 10^{-19}\text{ J}$
(C) $1\cdot25 \times 10^{-19}\text{ J}$
(D...
OR
The work function of a photosensitive surface is $2\cdot21\text{ eV}$. The value of threshold frequency for the surface is :
(A) $4\cdot8 \times 10^{14}\text{ Hz}$
(B) $5\cdot3 \times 10^{14}\text{ Hz}$
(C) $1\cdot9 \times 10^{15}\text{ Hz}$
(D) $1\cdot2 \times 10^{15}\text{ Hz}$
Photoelectric effect is phenomenon of the ejection of electrons when the radiation of suitable frequency is made to fall on the surface of a metal. When light of suitable wavelength falls on the emitter C given in the diagram, the photoelectrons are emitted. These photoelectrons are drawn to the col...
A beam of red light and a beam of blue light have equal intensities. It implies that :
(A) Red light beam has higher number of photons than that in blue light beam.
(B) Blue light beam has higher number of photons than that in red light beam.
(C) Both beams contain the same number of photons.
(D) Th...
Assertion (A) : If the maximum kinetic energy of an electron in a photoelectric experiment is one-fourth the energy of a photon of wavelength $\lambda$ incident on a surface, the work function of the surface is $\frac{3}{4} \frac{\text{hc}}{\lambda}$.
Reason (R) : Photoelectric emission can be expla...
(a) Use Einstein's photoelectron equation to explain the experimental features of photoelectric emissions.
(b) Light of wavelength $450\text{ nm}$ is incident on three metals A, B and C of work functions $3\cdot2\text{ eV}$, $2\cdot7\text{ eV}$ and $1\cdot75\text{ eV}$ respectively. Which metal(s) w...
The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio $\left$\frac{\lambda_\alpha}{\lambda_\text{p}}\right$$ of de Broglie wavelengths associated with them will be :
(A) $\frac{1}{16}$
(B) $\frac{1}{8}$
(C) $\frac{1}{4}$
(D) $\frac{1}{2}$
The threshold frequency for a given metal is $3.6 \times 10^{14}$ Hz. If monochromatic radiations of frequency $6.8 \times 10^{14}$ Hz are incident on this metal, find the cut-off potential for the photoelectrons.
(iv) (b) Which of the following metals exhibits photoelectric effect with visible light ?
(A) Caesium
(B) Zinc
(C) Cadmium
(D) Magnesium
The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio $\left$\frac{\lambda_{\alpha}}{\lambda_{ ext{p}}}
ight$$ of de Broglie wavelengths associated with them will be :
(A) $\frac{1}{16}$
(B) $\frac{1}{8}$
(C) $\frac{1}{4}$
(D) $\frac{1}{2}$
(iv) (a) Red light, yellow light and blue light of the same intensity are incident on a metal surface successively. $K_R$, $K_Y$ and $K_B$ represent the maximum kinetic energy of photoelectrons respectively, then :
(A) $K_R > K_Y > K_B$
(B) $K_Y > K_B > K_R$
(C) $K_B > K_Y > K_R$
(D) $K_R > K_B > K_...
The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio $\left$\frac{\lambda_{\alpha}}{\lambda_p}\right$$ of de Broglie wavelengths associated with them will be :
(A) $\frac{1}{16}$
(B) $\frac{1}{8}$
(C) $\frac{1}{4}$
(D) $\frac{1}{2}$
Which of the following metals exhibits photoelectric effect with visible light ?
(A) Caesium
(B) Zinc
(C) Cadmium
(D) Magnesium
Which of the following graphs shows the variation of photoelectric current I with the intensity of light ?
(A) [Graph showing a downward sloping line from I-axis to Intensity-axis]
(B) [Graph showing a horizontal straight line parallel to Intensity-axis]
(C) [Graph showing a straight line passing th...
The work function of a material is $2\cdot21\text{ eV}$. Which of the following \textbf{cannot} produce photoelectrons from it ?
(A) $\text{Red light}$
(B) $\text{Blue light}$
(C) $\text{Violet light}$
(D) $\text{Green light}$
The momentum (in $\text{kg m/s}$) of a photon of frequency $6\cdot0 \times 10^{14}\text{ Hz}$ is :
(A) $6\cdot63 \times 10^{-25}$
(B) $1\cdot326 \times 10^{-27}$
(C) $2\cdot652 \times 10^{-26}$
(D) $3\cdot978 \times 10^{-24}$
A laser beam of frequency $3\cdot0 \times 10^{14}\text{ Hz}$ produces average power of $9\text{ mW}$. Find (i) the energy of photon of the beam, and (ii) the number of photons emitted per second on an average by the source.
The de Broglie wavelength associated with an electron moving with energy $5\text{ eV}$ is :
(A) $0.75\text{ nm}$
(B) $1.2\text{ nm}$
(C) $2.4\text{ nm}$
(D) $0.55\text{ nm}$
The wavelength of a photon is equal to the wavelength associated with an electron. Both will have the same value of :
(A) energy
(B) angular momentum
(C) velocity
(D) linear momentum
Out of the four options given, in which transition will the emitted photon have the maximum wavelength ?
(A) $n = 4 \text{ to } n = 3$
(B) $n = 3 \text{ to } n = 2$
(C) $n = 2 \text{ to } n = 1$
(D) $n = 3 \text{ to } n = 1$
(a) Define 'work function' of a metal. How can its value be determined from a graph between stopping potential and frequency of the incident radiation ?
(b) The work function of a metal is $2.4 \text{ eV}$. A stopping potential of $0.6 \text{ V}$ is required to reduce the photocurrent to zero, in a ...
(a) Briefly explain Einstein's photoelectric equation.
(b) Four metals with their work functions are listed below :
$ ext{K} = 2\cdot3 ext{ eV}$, $ ext{Na} = 2\cdot75 ext{ eV}$, $ ext{Mo} = 4\cdot17 ext{ eV}$ and $ ext{Ni} = 5\cdot15 ext{ eV}$.
The radiation of wavelength $330 ext{ nm}$ from a laser...
Answer the following, giving reasons :
(a) The maximum kinetic energy of the photoelectrons is independent of the intensity of incident radiation.
(b) Photoelectric current increases with the increase in the intensity of the incident radiation.
(c) The stopping potential $V_0$ varies linearly with t...
The work function of Caesium is $2\cdot 14\text{ eV}$.
(a) Find the threshold frequency for Caesium.
(b) Find the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of $0\cdot 86\text{ V}$.
Monochromatic light of frequency $7.0 \times 10^{14}\text{ Hz}$ is produced by a laser. The power emitted is $21\text{ mW}$. Calculate (i) the energy of a photon in the light beam, and (ii) the number of photons per second, on an average, emitted by the source.
An electron of mass $m$ and charge $e$ is accelerated from rest through a potential $V$. Prove that, after acceleration, the de Broglie wavelength associated with the electron is proportional to $\frac{1}{\sqrt{V}}$.
(a) Draw a plot of frequency $\nu$ of incident radiations as a function of stopping potential $V_0$ for a given photo emissive material. What information can be obtained from the value of the intercept on the stopping potential axis ? (b) Calculate : (i) the momentum and (ii) de Broglie wavelength, ...
In a photoelectric experiment with a material of work function 2.1 eV, the stopping potential is found to be 2.5 V. The maximum kinetic energy of ejected photoelectrons is
(A) 0.4 eV
(B) 2.1 eV
(C) 2.5 eV
(D) 4.6 eV
(a) Mention any three features of results of experiment on photoelectric effect which cannot be explained using the wave theory of light.
(b) In his experiment on photoelectric effect, Robert A. Millikan found the slope of the cut-off voltage versus frequency of incident light plot to be $4.12 \time...
A light of wavelength $400 \text{ nm}$ is incident on metal surface whose work function is $3.0 \times 10^{-19} \text{ J}$. Calculate the speed of the fastest photoelectrons emitted.
Radiations of two frequencies are incident on a metal surface of work function 2.0 eV one by one. The energies of their photons are 2.5 eV and 4.5 eV respectively. Find the ratio of the maximum speed of the electrons emitted in the two cases.
The threshold wavelength of a metal is $450\text{ nm}$. Calculate (i) the work function of the metal in $\text{eV}$ and (ii) the maximum energy of the ejected photoelectrons in $\text{eV}$ by incident radiation of $250\text{ nm}$.
Which one out of the following transitions of an electron in Bohr's model of hydrogen atom will emit a photon with the greatest frequency ?
(A) $n = 3$ to $n = 1$
(B) $n = 3$ to $n = 2$
(C) $n = 4$ to $n = 3$
(D) $n = 4$ to $n = 2$
Assertion (A) : A photon behaves as a particle.
Reason (R) : A photon possesses both energy and momentum.
State postulates of Bohr model of hydrogen atom. Using Bohr's second postulate, show that the circumference of $\text{n}^{\text{th}}$ orbit in hydrogen atom is n times the de Broglie wavelength associated with the electron revolving in it.
30. A photon is a quantum of energy. The energy of a photon depends on its frequency ($\nu$). When light of suitable frequency is incident on a metal surface, photo-electrons are emitted from the surface. The minimum frequency is called threshold frequency ($\nu_0$) and the minimum energy required t...
(i) The packet of electromagnetic energy is called -
(A) Photon
(B) Neutron
(C) Molecule
(D) Quark
(ii) A photon has energy $3.3 \times 10^{-19}\text{ J}$. Its momentum is -
(A) $9.9 \times 10^{-11}\text{ kg.m/s}$
(B) $9.9 \times 10^{-26}\text{ kg.m/s}$
(C) $1.1 \times 10^{-27}\text{ kg.m/s}$
(D) $3.3 \times 10^{-25}\text{ kg.m/s}$
The work function of a metal is $2.14 \text{ eV}$. When light of frequency $6 \times 10^{14} \text{ Hz}$ is incident on the metal surface, photoemission of electrons occurs. The maximum kinetic energy of the emitted electrons is –
(A) $0.34 \times 10^{-18} \text{ J}$
(B) $0.40 \times 10^{-17} \text{...
The work function of a metal is $2.21 \text{ eV}$. The threshold frequency for the metal is
(A) $2.1 \times 10^{13} \text{ Hz}$
(B) $3.2 \times 10^{13} \text{ Hz}$
(C) $5.3 \times 10^{14} \text{ Hz}$
(D) $4.1 \times 10^{15} \text{ Hz}$
Two beams, A and B whose photon energies are 3.3 eV and 11.3 eV respectively, illuminate a metallic surface (work function 2.3 eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is : (A) 3 (B) 9 (C) $\frac{1}{3}$ (D) $\frac{1}{9}$
Consider a neutron (mass $m$) of kinetic energy $E$ and a photon of the same energy. Let $\lambda_n$ and $\lambda_p$ be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for $\frac{\lambda_n}{\lambda_p}$.
Assertion (A): de Broglie's wavelength of a freely falling body keeps decreasing with time.
Reason (R): The momentum of the freely falling body increases with time.
A platinum surface having work function $5.63 \text{ eV}$ is illuminated by a monochromatic source of $1.6 \times 10^{15} \text{ Hz}$. What will be the minimum wavelength associated with the ejected electron.
Case Study Based Question: Photoelectric effect. It is the phenomenon of emission of electrons from a metallic surface when light of a suitable frequency is incident on it. The emitted electrons are called photoelectrons.
The threshold frequency for photoelectric effect on sodium corresponds to a wavelength of $500\text{ nm}$. Its work function is about (A) $4 \times 10^{-19}\text{ J}$ (B) $1\text{ J}$ (C) $2 \times 10^{-19}\text{ J}$ (D) $3 \times 10^{-19}\text{ J}$
The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy $6\text{ eV}$ fall on it is $4\text{ eV}$. The stopping potential is (A) $2\text{ V}$ (B) $4\text{ V}$ (C) $6\text{ V}$ (D) $10\text{ V}$
The minimum energy required to remove an electron from a substance is called its (A) work function (B) kinetic energy (C) stopping potential (D) potential energy
The work function for a photosensitive surface is $3.315\text{ eV}$. The cut-off wavelength for photoemission of electrons from this surface is :
(A) $150\text{ nm}$
(B) $200\text{ nm}$
(C) $375\text{ nm}$
(D) $500\text{ nm}$
de Broglie wavelength $\lambda$ as a function of $\frac{1}{\sqrt{K}}$, for two particles of masses $m_1$ and $m_2$ are shown in the figure. Here, K is the energy of the moving particles. (a) What does the slope of a line represent? (b) Which of the two particles is heavier? (c) Is this graph also va...
A photosensitive surface has a work function of $2\cdot00\text{ eV}$. The maximum kinetic energy of electrons ejected from this surface by radiation of wavelength $300\text{ nm}$ is:
(A) $0\cdot54\text{ eV}$
(B) $1\cdot07\text{ eV}$
(C) $1\cdot61\text{ eV}$
(D) $2\cdot14\text{ eV}$
(a) Briefly explain de Broglie hypothesis for wave nature of matter.
(b) Find the ratio of de Broglie wavelength associated with a proton and an alpha particle when both are
(i) accelerated from rest through the same potential difference, and
(ii) moving with the same kinetic energy.
The momentum (in SI units) associated with a photon of energy $1.5\text{ eV}$ is :
(A) $4 \times 10^{-27}$
(B) $8 \times 10^{-28}$
(C) $2 \times 10^{-30}$
(D) $6 \times 10^{-29}$
Assertion (A) : The kinetic energy of the emitted photoelectrons depends upon the work function of the surface. Reason (R) : The maximum value of kinetic energy of photoelectrons is the difference of energy of incident photons and work function of the surface.
The threshold frequency for a metal surface for photoelectric emission is $4 \times 10^{14}\text{ Hz}$. When a light of frequency $\nu$ is incident upon it, the emitted photoelectrons are stopped by a stopping potential of $4.98\text{ V}$. Calculate :
(a) work function of the metal, and
(b) the valu...
Which one of the given graphs correctly represents the variation of photoelectric current with the intensity of incident radiation, keeping other parameters fixed ?
Radiations of frequency $3.0 \times 10^{15} \text{ Hz}$ are incident on a photosensitive surface of threshold frequency $1.0 \times 10^{15} \text{ Hz}$. Calculate : (a) work function of the surface (b) maximum kinetic energy of photoelectrons
The figure shows the variation of stopping potential $V_0$ with frequency $\nu$ of incident radiation, for three materials $M_1$, $M_2$ and $M_3$ with work functions $\phi_1$, $\phi_2$ and $\phi_3$ respectively. Then :
(A) $\phi_1 > \phi_2 > \phi_3$
(B) $\phi_2 > \phi_3 > \phi_1$
(C) $\phi_3 > \phi_...
Light of wavelength 500 nm is incident on caesium metal (work function 2.14 eV) and photoemission of electrons occurs. Calculate the (i) kinetic energy (in eV) of the fastest electrons and (ii) stopping potential for this situation. (Take hc = 1240 eV.nm)
The wavelength of matter wave associated with an electron of kinetic energy K is $\lambda$. If the kinetic energy of the electron is doubled, the associated wavelength becomes :
(A) $\frac{\lambda}{\sqrt{2}}$
(B) $\frac{\lambda}{2}$
(C) $\sqrt{2} \lambda$
(D) 2 $\lambda$
Light of wavelength $600\text{ nm}$ is incident on potassium (work function $2.3\text{ eV}$). Will photoemission of electrons occur ? What is the longest wavelength that will cause photoemission of electrons ? (Take $\text{hc} = 1240\text{ eV. nm}$)
A proton and $\alpha$-particle are accelerated through different potentials $V_1$ and $V_2$ respectively so that they have the same de Broglie wavelengths. Find $\frac{V_1}{V_2}$.
What are matter waves? A proton, an electron and an $\alpha$-particle have the same kinetic energy. Write the de Broglie wavelengths associated with them in increasing order.
The ratio of de Broglie wavelengths of a proton and a deuteron accelerated by potential $V_p$ and $V_d$ respectively, $\left$ \frac{\lambda_p}{\lambda_d} \right$$ is $\frac{1}{2}$. Find $\frac{V_p}{V_d}$.
(a) Write Einstein's photoelectric equation. How did Millikan prove the validity of this equation? (b) Explain the existence of threshold frequency of incident radiation for photoelectric emission from a given surface.
The variation of the stopping potential $(V_0)$ with the frequency $(v)$ of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will be maximum for met...
A photosensitive surface of work function 2.1 eV is irradiated by radiation of wavelength 150 nm. Calculate (i) the threshold wavelength, (ii) energy (in eV) of an incident photon, and (iii) maximum kinetic energy of emitted photoelectron.
The threshold frequency for a metal is $3.0 \times 10^{14}\text{ Hz}$. A beam of frequency $9.0 \times 10^{14}\text{ Hz}$ is incident on the metal. Calculate (i) the work function (in eV) of the metal and (ii) the maximum speed of photoelectrons.
In the photoelectric effect, electrons are emitted from a given metal surface when the incident radiation has a certain minimum value of :
(A) frequency
(B) intensity
(C) wavelength
(D) angle of incidence
Assertion (A) : Work functions of different metals are different.
Reason (R) : Metals differ in their conductivity.
Answer the following giving reasons :
(a) The speed of emitted electrons depends on the work function of the photosensitive surface, for the incident radiation of a given frequency.
(b) The stopping potential ($V_0$) increases linearly with the frequency of incident radiation, for a given photosensi...
A metallic plate exposed to white light emits electrons. For which of the following colours of light, the stopping potential will be maximum?
(a) Blue
(b) Yellow
(c) Red
(d) Violet
Assertion (A): For the radiation of a frequency greater than the threshold frequency, photoelectric current is proportional to the intensity of the radiation. Reason (R): Greater the number of energy quanta available, greater is the number of electrons absorbing the energy quanta and greater is numb...
The wavelength $\lambda$ of a photon and the de Broglie wavelength of an electron of mass m have the same value. Show that the energy of the photon is $\frac{2\lambda mc}{h}$ times the kinetic energy of the electron, where c and h have their usual meanings.
The energy of a photon in a beam of red light with a wavelength of $6.60 \times 10^{-7} \text{ m}$ is close to : (a) $4.42 \times 10^{-19} \text{ J}$ (b) $4.0 \times 10^{-19} \text{ J}$ (c) $2.19 \times 10^{-19} \text{ J}$ (d) $3.0 \times 10^{-19} \text{ J}$
A photon absorbed by a hydrogen atom excites it from $n = 3$ level to $n = 5$ level. The energy of the photon is : (a) $+0.97 \text{ eV}$ (b) $-0.97 \text{ eV}$ (c) $+1.51 \text{ eV}$ (d) $-0.54 \text{ eV}$
Assertion ($A$) : The energy ($E$) and momentum ($p$) of a photon are related as $p = \frac{h}{E}$.\nReason ($R$) : Photons behave as a wave.
State Bohr's postulates of hydrogen atom. How is a photon emitted by an excited hydrogen atom ?
Briefly explain how Einstein's photoelectric equation accounts for all observations on photoelectric effect.
Which of the following figures represents the variation of a particle's momentum with the de Broglie wavelength associated with it ?
(a) [Graph showing a linear increase of $P$ with $\lambda$]
(b) [Graph showing a hyperbolic decrease of $P$ with $\lambda$]
(c) [Graph showing a linear decrease of $P$...
Light of frequency $1.5
u_0$ is incident on a photosensitive material of threshold frequency $
u_0$. If the frequency of the incident radiation is kept constant and intensity is increased, the photo current will :
(a) increase
(b) decrease
(c) not change
(d) first decrease and then become zero
Light of wavelength $3500 \text{ \AA}$ is incident on two metals A and B. Which of them will yield photoelectrons, if their work functions are $4.2 \text{ eV}$ and $1.9 \text{ eV}$ respectively ? Make the necessary calculations to justify your answer.
The figure shows the variation of stopping potential $V_0$ with frequencies of incident monochromatic beam for a metal. Such a graph was first obtained by R.A. Millikan in 1916 for sodium.
Explain how, using Einstein's photoelectric equation and the graph, you can obtain the value of (i) Planck's c...
Which of the following figures represents the variation of a particle's momentum with the de Broglie wavelength associated with it ?
(a) [graph a]
(b) [graph b]
(c) [graph c]
(d) [graph d]
Light of frequency $1.5\ \nu_0$ is incident on a photosensitive material of threshold frequency $\nu_0$. If the frequency of the incident radiation is kept constant and intensity is increased, the photo current will : (a) increase (b) decrease (c) not change (d) first decrease and then become zero
Light of wavelength $3500 \; \text{\AA}$ is incident on two metals A and B. Which of them will yield photoelectrons, if their work functions are $4.2 \; \text{eV}$ and $1.9 \; \text{eV}$ respectively ? Make the necessary calculations to justify your answer.
The figure shows the variation of photoelectric current (I) versus applied voltage (V) for two photosensitive materials and for two different intensities of the incident radiation. Identify the pairs of curves that correspond to different materials for same intensity of incident radiation. Justify y...
Which of the following figures represents the variation of a particle's momentum with the de Broglie wavelength associated with it ? (a) [Graph of P vs $\lambda$ as straight line passing through origin] (b) [Graph of P vs $\lambda$ as rectangular hyperbola] (c) [Graph of P vs $\lambda$ as downward s...
Light of frequency $1\cdot 5 \; \nu_0$ is incident on a photosensitive material of threshold frequency $\nu_0$. If the frequency of the incident radiation is kept constant and intensity is increased, the photo current will :
(a) increase
(b) decrease
(c) not change
(d) first decrease and then become...
Light of wavelength $3500 \text{ \AA}$ is incident on two metals A and B. Which of them will yield photoelectrons, if their work functions are $4\cdot2 \text{ eV}$ and $1\cdot9 \text{ eV}$ respectively ? Make the necessary calculations to justify your answer.
A beam of high energy photons, each of energy of E is incident on a metal surface and electrons are ejected from the surface. Assuming that the work function of the metal, $\phi$ is negligible, find the relation between the de Broglie wavelength $\lambda$ associated with photoelectrons and the energ...
The work function of potassium is $2.3\text{ eV}$ and threshold wavelength for it is $540\text{ nm}$. The threshold wavelength for a metal whose work function is $4.6\text{ eV}$ will be :
(a) $135\text{ nm}$
(b) $270\text{ nm}$
(c) $540\text{ nm}$
(d) $1080\text{ nm}$
(a) Write Einstein's photoelectric equation. Use it to :
(i) explain the existence of threshold frequency for a given photosensitive surface.
(ii) show that the stopping potential, $V_0$ varies linearly with the frequency $\nu$ of incident radiation.
Explain how the value of Planck's constant can be...
Assertion (A) : The photoelectric current increases with increase in intensity of incident radiation, keeping the frequency of the incident radiation and the accelerating potential fixed.
Reason (R) : The number of photoelectrons emitted per second is directly proportional to the intensity of incide...
Ultra-violet light of wavelength $200\text{ nm}$ from a source is incident on a metal surface. If the stopping potential is $-2.5\text{ V}$, (a) calculate the work function of the metal, and (b) How would the surface respond to a high intensity red light of wavelength $6328\text{ \AA}$ produced by a...
The work function for a metal surface is 4.14 eV. The threshold wavelength for this metal surface is: (i) $4125 \text{ Å}$ (ii) $2062.5 \text{ Å}$ (iii) $3000 \text{ Å}$ (iv) $6000 \text{ Å}$
The ground state energy of hydrogen atom is -13.6 eV. The photon emitted during the transition of electron from n=3 to n=1 state, is incident on a photosensitive material of unknown work function. The photoelectrons are emitted from the material with the maximum kinetic energy of 9 eV. Calculate the...
OR (b) Photoelectric emission occurs when a surface is irradiated with the radiation of frequency (i) $\nu_1$, and (ii) $\nu_2$. The maximum kinetic energy of the electrons emitted in the two cases are K and 2K respectively. Obtain the expression for the threshold frequency for the surface.
(a) Give an example each of a metal from which photoelectric emission takes place when irradiated by (i) UV light (ii) visible light. (b) The work function of a metal is $4.50\text{ eV}$. Find the frequency of light to be used to eject electrons from the metal surface with a maximum kinetic energy o...
(b) In photon picture of light, what determines the intensity of light ?
(b) Lights of wavelengths $430\text{ nm}$, $450\text{ nm}$ and $660\text{ nm}$ are incident on a metal surface whose threshold wavelength is $600\text{ nm}$. In which case/cases will photoemission take place and why ? Calculate the threshold frequency of the metal surface.
(a) Define the terms 'distance of closest approach' and 'impact parameter'. OR (b) Explain briefly any two features of photoelectric effect.
A beam of light of wavelength $500 \text{ nm}$ is incident on a photosensitive surface. If the threshold wavelength for the surface is $663 \text{ nm}$, then calculate : (a) the work function for the surface, and (b) the maximum kinetic energy (in eV) of the photoelectrons.
(a) Briefly explain how energy is released due to proton-proton cycle in the interior of the Sun. OR (b) How is the photoelectric current affected with (i) the increase of the intensity of the incident radiation, keeping its frequency same ? (ii) the decrease of the frequency of the incident radiati...
(a) Write two differences between matter waves and electromagnetic waves.
(b) Find the ratio of de Broglie wavelengths associated with deuterium and tritium if both have the same kinetic energies.