Dual Nature of Matter and Radiation — JEE Main PYQs

The graph shows variation of stopping potential $V_0$ with the frequency $\nu$ of the incident radiation for three photosensitive metals $X_1$, $X_2$ and $X_3$. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

[Figure: Graph of stopping potential $V_0$ versus frequency $\nu$ showing three parallel straight lines for metals $X_1$, $X_2$, $X_3$ with threshold frequencies at 1.0, 1.5 and 2 ($\times 10^{14}$ Hz) respectively]

The de Broglie wavelength associated with an electron accelerated through a potential difference $V$ is $\lambda_e$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $\lambda_p$. If their corresponding masses are $m_e$ and $m_p$, respectively, then the ratio of their de Broglie wavelengths $\left(\frac{\lambda_e}{\lambda_p}\right)$ is _______.

An electron of mass $m$ is moving in an electric field $\vec{E} = -2E_0\hat{i}$ ($E_0$ = constant $> 0$), with an initial velocity $\vec{V} = v_0\hat{i}$ ($v_0$ = constant $> 0$). If $\lambda_0 = \dfrac{h}{4mv_0}$, its de Broglie wavelength at time $t$ is ______.

($e$ = charge of electron)

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 $\alpha \times 10^{-19}$ J. The value of $\alpha$ is _____.

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

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20\%$. The de Broglie wavelength of electron in the medium is $\alpha \lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is __________.

The de Broglie wavelength for an electron accelerated through the potential difference of $V_1$ volt is $\lambda_1$. When the potential difference is changed to $V_2$ volt, the associated de Broglie wavelength is increased by 50%. If $(V_1/V_2) = (9/\alpha)$, then the value of $\alpha$ is ________.

$K_1$ 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 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)

An electron with mass 'm' with an initial velocity $(t=0)$ $\vec{v}=v_0\,\hat{i}\ (v_0>0)$ enters a magnetic field $\vec{B}=B_0\,\hat{j}$. If the initial de-Broglie wavelength at $t=0$ is $\lambda_0$ then its value after time 't' would be :

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

A photoemissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_o$. Expression for de-Broglie wavelength is given by :

(m : mass of the electron, h : Planck's constant and c : speed of light)

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$-\sigma$' .The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of n 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

A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity $2.21 \times 10^{6}$ m/s. Under the matter wave consideration, the particle will behave closely like _____. ($h = 6.63 \times 10^{-34}$ J.s)

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 2V, what is the wavelength of the em-wave ?

(Given hc = 1242 eVnm where h is the Planck's constant and c is the speed of light in vaccum.)

An electron of mass 'm' with an initial velocity $\vec{v}=v_0\hat{i}\,(v_0>0)$ enters an electric field $\vec{E}=-E_o\hat{k}$. If the initial de Broglie wavelength is $\lambda_0$, the value after time t would be

In photoelectric effect, the stopping potential $(\mathrm{V}_0)$ v/s frequency $(\nu)$ curve is plotted.

(h is the Planck's constant and $\phi_0$ is work function of metal)

(A) $\mathrm{V}_0$ v/s $\nu$ is linear.

(B) The slope of $\mathrm{V}_0$ v/s $\nu$ curve $= \frac{\phi_0}{h}$

(C) h constant is related to the slope of $\mathrm{V}_0$ v/s $\nu$ line.

(D) The value of electric charge of electron is not required to determine h using the $\mathrm{V}_0$ v/s $\nu$ curve.

(E) The work function can be estimated without knowing the value of h.

Choose the correct answer from the options given below :

The ratio of the power of a light source $\mathrm{S}_1$ to that of the light source $\mathrm{S}_2$ is 2. $\mathrm{S}_1$ is emitting $2 \times 10^{15}$ photons per second at 600 nm. If the wavelength of the source $\mathrm{S}_2$ is 300 nm, then the number of photons per second emitted by $\mathrm{S}_2$ is ______ $\times 10^{14}$.

A proton of mass '$m_p$' has same energy as that of a photon of wavelength '$\lambda$'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

Which of the following phenomena can not be explained by wave theory of light?

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light ($\mathrm{I_1} < \mathrm{I_2}$) of same wavelengths :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements :

[Figure: graph of stopping potential $V_0$ versus frequency $\nu$ showing two parallel straight lines for materials $M_1$ and $M_2$, with the line for $M_1$ to the left of $M_2$]

Statement I : Figure shows the variation of stopping potential with frequency ($\nu$) for the two photosensitive materials $M_1$ and $M_2$. The slope gives value of $\frac{h}{e}$, where h is Planck's constant, e is the charge of electron.

Statement II : $M_2$ will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency.

In the light of the above statements, choose the most appropriate answer from the options given below.

Which of the following statement is not true about stopping potential $(V_0)$ ?

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

When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV, electron emission takes place. The stopping potential is : (Given $hc = 1240\ \mathrm{eV\,nm}$)

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume $h = 6.63 \times 10^{-34}$ J s, $\mathrm{m_e} = 9.0 \times 10^{-31}$ kg and $\mathrm{m_p} = 1836$ times $\mathrm{m_e}$)

A proton and an electron have the same de Broglie wavelength. If $\mathrm{K_p}$ and $\mathrm{K_e}$ be the kinetic energies of proton and electron respectively, then choose the correct relation :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

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

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :

Monochromatic light of frequency $6 \times 10^{14}$ Hz is produced by a laser. The power emitted is $2 \times 10^{-3}$ W. How many photons per second on an average, are emitted by the source ?

(Given $h = 6.63 \times 10^{-34}$ Js)

A convex lens of focal length 40 cm forms an image of an extended source of light on a photo-electric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

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

For the photoelectric effect, the maximum kinetic energy $(E_k)$ of the photoelectrons is plotted against the frequency $(\nu)$ of the incident photons as shown in figure. The slope of the graph gives

[Figure: straight-line graph of $E_k$ (y-axis) versus $\nu$ (x-axis), intersecting the $\nu$-axis at a positive intercept and making angle $\theta$ with it]

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

In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be: