Photoelectric Effect: Einstein's Equation

A ray of light with wavelength $\lambda$ is incident on three different photoelectric cells namely 1,2 and 3. The threshold wavelength of these photoelectric cells are $\lambda_1, \lambda_2$, and $\lambda_3$, respectively and the magnitude of stopping potentials of these cells are $V_1, V_2$ and $V_3$, respectively. The relation between $\lambda$ and threshold wavelengths are $\lambda_1 < \lambda, \lambda_2 > \lambda$ and $\lambda_3 \gg \lambda$. The correct option is:

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 $6.6 \times 10^{-34}\text{ J s}$)

Light is incident on a metallic plate having work function $110 \times 10^{-20}\text{ J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s. $(h = 6.63 \times 10^{-34}\text{ J.s})$.

For a photosensitive material, work function is '$W_0$' and stopping potential is 'V'. The wavelength of the incident radiation is (h=Planck's constant, c = velocity of light, e = electronic charge)

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha \times 10^{-19}\text{ J}$. The value of $\alpha$ is ______.

$\left(h = 6.62 \times 10^{-34}\text{ J s},\ e = 1.6 \times 10^{-19}\text{ C}\right.$ and $\left.c = 3 \times 10^{8}\text{ m/s}\right)$

In case of photoelectric emission from certain metal, the cutoff frequency is $\nu$. If the radiation of frequency $3\nu$ is incident on the metal plate, the maximum possible velocity of the emitted electrons will be ($m$ = mass of electron, $h$ = Planck's constant)

Energy of the incident photons on the photosensitive metal surface is 3W and then 5W where 'W' is the work function of that metal. The ratio of velocities of the emitted photoelectrons is

When photons of energy $h\nu$ fall on a metal plate of work function $W_0$, photoelectrons of maximum kinetic energy K are ejected. If the frequency of radiation is doubled, the maximum kinetic energy of ejected photoelectrons will be

The frequency of the incident light falling on a photosensitive metal plate is doubled, the kinetic energy of the emitted photoelectrons is

A light wave described by $E = 60\left[\sin\left(3 \times 10^{15}\right)t + \sin\left(12 \times 10^{15}\right)t\right]$ (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately)

______ eV. $\left(h = 6.6 \times 10^{-34}\right.$ J.s. and $\left.e = 1.6 \times 10^{-19}\text{ C}\right)$

When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V$. If the surface is now illuminated with a radiation of wavelength $4\lambda$, the stopping potential $\left(\frac{V}{8}\right)$. The threshold wavelength for the surface is

When a certain metal surface is illuminated with a light of wavelength $\lambda$, the stopping potential is $V$. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is $\left(\frac{V}{3}\right)$. The threshold wavelength for the surface is

When light of wavelength '$\lambda$' is incident on a photosensitive surface, the stopping potential is 'V'. When a light of wavelength $1.5\lambda$ is incident on the same surface, the stopping potential is ' $\frac{V}{4}$'. Threshold wavelength for the surface is

A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $(\lambda/3)$. If the maximum kinetic energy of the emitted photo electrons in the second case is $4$ times that in the first case, the work function of the surface of the material is ($h$ = Planck's constant, $c$ = speed of light)

When a metallic surface is illuminated with a radiation of wavelength '$\lambda$', the stopping potential is 'V'. If the same surface is illuminated with radiation of wavelength $6\lambda$, the stopping potential is $\left(\frac{V}{12}\right)$. The threshold wavelength for the surface is

For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_0$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potential becomes $V_0$. The threshold wavelength for photoelectric emission for the given metal is $\alpha\lambda$. The value of $\alpha$ is ______.

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V. The wavelength of first light is ______ m.

$\left(h = 6.63 \times 10^{-34}\text{ J.s}, e = 1.6 \times 10^{-19}\text{ C}, c = 3 \times 10^{8}\text{ m/s}\right)$

Radiation of wavelength $\lambda$, is incident on a photocell. The fastest emitted electron has speed $v$. If the wavelength is changed to $\frac{3\lambda}{4}$, the speed of the fastest electron will be

Energy of the incident photon on the metal surface is $3W$ and then $5W$, where $W$ is the work function of that metal. The ratio of velocities of emitted photoelectrons is

Two identical photocathodes receive light of frequencies $n_1$ and $n_2$. If the velocities of the emitted photoelectrons of mass m are $V_1$ and $V_2$ respectively, then ($h$ = Planck's constant)

When a light of wavelength '$\lambda$' falls on the emitter of a photosensitive surface, maximum speed of emitted photoelectrons is 'V'. If the incident wavelength is changed to '$2\lambda/3$', maximum speed of emitted photoelectrons will be

The threshold frequency of metal is $f_0$. When the light of frequency $2f_0$ is incident on the metal plate, the maximum velocity of photoelectron is $v_1$. When the frequency of incident radiation is increased to $5f_0$ the maximum velocity of photoelectrons emitted is $v_2$. The ratio $v_1$ to $v_2$ is

Light of wavelength $\lambda$ strikes a photoelectric surface and electrons are ejected with an energy $E$. If $E$ is to be increased to exactly twice its original value, the wavelength changes to $\lambda_1$ where

The maximum kinetic energies of photoelectrons emitted are $K_1$ and $K_2$ when light of wavelength $\lambda_1$ and $\lambda_2$ respectively are incident on a metallic surface. If $\lambda_1 = 3\lambda_2$ then

Photoelectric emission is observed from a metallic surface for frequencies $\nu_1$ and $\nu_2$ of the incident light rays ($\nu_1 > \nu_2$). If the ratio of maximum value of kinetic energy of the photoelectron emitted in first case to that in second case 3: K, then the threshold frequency of the metallic surface is

Photoelectrons are emitted from two similar metal plates when wavelengths $\lambda_1$ and $\lambda_2$ are incident on them ($\lambda_1 = 1.5\lambda_2$). If maximum kinetic energy of emitted photoelectrons is $E_1$ and $E_2$ respectively then

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays ($v_1 > v_2$). If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $k : 1$, then what is the threshold frequency of the metallic surface?

$K_1$ and $K_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $\lambda_1$ and $\lambda_2$, respectively. If $\lambda_1 = 2\lambda_2$ then the work function of material is given by:

A photon of energy $10$ units ejects a photo-electron from a metal surface whose work function is $\Phi_0$. If an electron(e) having maximum kinetic energy enters into a uniform magnetic field of induction(B) in a direction perpendicular to the field and describes a circular path of radius R, then radius R is {$m =$mass of electron}

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to that of copper is nearest to

Light of wavelength ' $\lambda$ ' falls on a metal having work function $\frac{hc}{\lambda_0}$. Photoelectric effect will take place only if ( $\lambda_0$ is the threshold wavelength)

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

The maximum velocity of the photoelectrons emitted by a metal surface is $9 \times 10^{5}\text{ m/s}$. The value of ratio of charge (e) to mass (m) of the photoelectron is $1.8 \times 10^{11}\text{ C/kg}$. The value of stopping potential in volt is

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V, what is the wavelength of the em-wave? (Given $hc = 1242\text{ eV nm}$ where h is the Planck's constant and c is the speed of light in vacuum.)

Energy of the incident photons on the metal surface is initially 4 W and then 6 W where $W$ is the work function of that metal. The ratio of velocities of emitted photoelectrons is

Photoelectric emission takes place from a certain metal at threshold frequency $\nu$. If the radiation of frequency $4\nu$ is incident on the metal plate, the maximum velocity of the emitted photoelectrons will be ( $m =$ mass of photoelectron, $h =$ Planck's constant)

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $V_1$ and $V_2$ respectively. The ratio $V_1 : V_2$ is

When a metal surface is illuminated by light of wavelength $\lambda_1$ and $\lambda_2$, the maximum velocities of photoelectrons ejected are V and 2 V respectively. The work function of the metal is ( $h =$ Planck's constant, $c =$ velocity of light, $\lambda_1 > \lambda_2$)

When a photosensitive metal surface is illuminated with radiation of wavelength ' $\lambda_1$ ', the stopping potential is ' $V_1$ '. If the same surface is illuminated with radiation of wavelength ' $3\lambda_1$ ', the stopping potential is $\frac{V_1}{6}$. The threshold wavelength for the photosensitive metal surface is

A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV. If the same surface is illuminated by a light source of wavelength $\frac{\lambda}{2}$, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV)

A photosensitive surface has work function $\phi$. If photon of energy $3\phi$ falls on this surface, the electron comes out with maximum velocity of $4 \times 10^{6}\text{ m/s}$ When photon energy is increased to $7\phi$ then maximum velocity of photoelectron will be

When a light of wavelength $\lambda$ falls on the emitter of a photocell, maximum speed of emitted photoelectrons is V. If the incident wavelength is changed to $\frac{2\lambda}{3}$, maximum speed of emitted photoelectrons will be:

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays $(v_1 > v_2)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $1 : k$, then the threshold frequency of metallic surface is

On a photosensitive material, when frequency of incident radiation is increased by $20\%$, maximum kinetic energy of emitted photoelectrons increases from 0.4 eV to 0.7 eV. The work function of the material is

Light of wavelength $\lambda$ strikes a photoelectric surface and electrons are ejected with energy E. If $E$ is to be increased to twice the original value, the wavelength changes to $\lambda_1$

If the electron in hydrogen atom jumps from third Bohr orbit to ground state directly and the difference between energies of the two states is radiated in the form of photons. If the work function of the material is 4.1 eV, then stopping potential is nearly

[Energy of electron in $n$th orbit $= \frac{-13.6}{n^2}\text{ eV}$ ]

A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point $B$. The distance between $A$ and $B$ is: (Given: The magnitude of charge of an electron is e and mass is $m, h$ is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

The work function of a substance is $3.0\text{ eV}$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

The threshold frequency of a metal with work function $6.63\text{ eV}$ is:

For a photosensitive material, work function is ' $W_0$ ' and stopping potential is ' V '. The wavelength of incident radiation is ( $h =$ Planck's constant, $c =$ velocity of light, $e =$ electronic charge)

The stopping potential for a photelectric emission process is 10 V. The maximum kinetic energy of the electrons ejected in the process is [Charge on electron $e = 1.6 \times 10^{-19}\text{ C}$ ]

UV light of $4.13\text{ eV}$ is incident on a photosensitive metal surface having work function $3.13\text{ eV}$. The maximum kinetic energy of ejected photoelectrons will be:

When UV light of wavelength $300\text{ nm}$ is incident on the metal surface having work function $2.13\text{ eV}$, electron emission takes place. The stopping potential is:

(Given hc $= 1240\text{ eV nm}$)

In photoelectric experiment energy of $2.48\text{ eV}$ irradiates a photo sensitive material. The stopping potential was measured to be $0.5\text{ V}$. Work function of the photo sensitive material is:

Two photons having energies twice and thrice the work function of metal are incident one after another on the metal surface. Then the ratio of maximum velocities of the photoelectrons emitted in the two cases is respectively

The frequency of incident light falling on a photosensitive material is doubled, the K.E. of the emitted photoelectrons will be

When photons of energy hv fall on a photosensitive surface of work function $E_0$, photoelectrons of maximum energy $k$ are emitted. If the frequency of radiation is doubled the maximum kinetic energy will be equal to ( $h =$ Planck's constant)

If $\phi$ is the work function of photosensitive material in $\text{eV}$ and light of wavelength of numerical value $\lambda = \frac{hc}{e}$ metre, is incident on it with energy above its threshold value at an instant then the maximum kinetic energy of the photo-electron ejected by it at that instant (Take $h$-Plank's constant, $c$-velocity of light in free space) is (in SI units):

When a certain metallic surface is illuminated with monochromatic light wavelength $\lambda$, the stopping potential for photoelectric current is $4V_0$. When the same surface is illuminated with light of wavelength $3\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photoelectric effect is

A photoelectric surface is illuminated successively by monochromatic light of Wavelength $\lambda$ and $(\lambda/3)$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 4 times that in the first case, the work function of the surface of the material is $(h =$ Planck's constant, $c =$ speed of light $)$

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

When a photosensitive surface is irradiated by lights of wavelengths ' $\lambda_1$ ' and ' $\lambda_2$ ', kinetic energies of the emitted photoelectrons is ' $E_1$ ' and ' $E_2$ ' respectively. The work function of the photosensitive surface is

When a metallic surface is illuminated with a radiation of wavelength ' $\lambda$ ', the stopping potential is ' $V$ '. If the same surface is illuminated with radiation of wavelength ' $3\lambda$ ', the stopping potential is ' $\left(\frac{V}{6}\right)$ '. The threshold wavelength for the surface is

When a metal surface is illuminated by light of wavelength $\lambda$, the stopping potential is $8\text{ V}$. When the same surface is illuminated by light of wavelength $3\lambda$, stopping potential is $2\text{ V}$. The threshold wavelength for this surface is:

Two identical photocathodes receive light of frequencies ' $n_1$ ' and ' $n_2$ '. If the velocities of the emitted photoelectrons of mass ' $m$ ' are ' $V_1$ ' and ' $V_2$ ' respectively, then ( $h =$ Planck's constant)

A photosensitive metallic surface has work function $\phi$. If photon of energy $3\phi$ falls on the surface, the electron comes out with a maximum velocity of $6 \times 10^{6}\text{ m/s}$. When the photon energy is increased to $9\phi$, then maximum velocity of photoelectrons will be

The threshold frequency of a metal is ' $F_0$ '. When light of frequency $2F_0$ is incident on the metal plate, the maximum velocity of photoelectron is ' $V_1$ '. When the frequency of incident radiation is increased to ' $5F_0$ ', the maximum velocity of photoelectrons emitted is ' $V_2$ '. The ratio of $V_1$ to $V_2$ is

The work function of metal ' $A$ ' and ' $B$ ' are in the ratio $1 : 2$. If light of frequency ' $f$ ' and ' $2f$ ' is incident on surface ' $A$ ' and ' $B$ ' respectively, then the ratio of kinetic energies of emitted photo electrons is

When a light of wavelength $300\text{ nm}$ falls on a photoelectric emitter, photo electrons are emitted. For another emitter light of wavelength $600\text{ nm}$ is just sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is

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

The difference between threshold wavelengths for two metal surfaces $\text{A}$ and $\text{B}$ having work function $\phi_A = 9\text{ eV}$ and $\phi_B = 4.5\text{ eV}$ in $\text{nm}$ is:

$\{$ Given, hc $= 1242\text{ eVnm}\}$

If the two metals $\text{A}$ and $\text{B}$ are exposed to radiation of wavelength $350\text{ nm}$. The work functions of metals $\text{A}$ and $\text{B}$ are $4.8\text{ eV}$ and $2.2\text{ eV}$. Then choose the correct option.

The threshold wavelength for photoelectric emission from a material is 5500 $\mathring{A}$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp

B. 10 W infra-red lamp

C. 75 W ultra-violet lamp

D. 10 W ultra-violet lamp

Choose the correct answer from the options given below:

A metal surface of work function $1.13\text{ eV}$ is irradiated with light of wavelength $310\text{ nm}$. The retarding potential required to stop the escape of photoelectrons is [Take $\frac{hc}{e} = 1240 \times 10^{-9}\text{ SI}$ units]