JEE Main 2022 — Modern Physics

In hydrogen atom, the ratio of radii of first and second orbit is:

The de Broglie wavelength of a particle with momentum p is

The work function of a metal is 4.2 eV. The maximum kinetic energy of photoelectrons when light of wavelength 200 nm falls on it is:

A proton, a neutron, an electron and an $\alpha$-particle have same energy. If ${\lambda }_{p},{\lambda }_{n},{\lambda }_{e}$ and ${\lambda }_{\alpha }$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following

The kinetic energy of emitted electron is $E$ when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength:

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

The ratio of wavelengths of proton and deuteron accelerated by potential ${V}_{p}$ and ${V}_{d}$ is $1:\sqrt{2}$. Then, the ratio of ${V}_{p}$ to ${V}_{d}$ will be

A parallel beam of light of wavelength $900\mathrm{nm}$ and intensity $100{\mathrm{Wm}}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1{\mathrm{cm}}^{2}$ area perpendicular to the beam in one second is

Let ${K}_{1}$ and ${K}_{2}$ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength ${\lambda }_{1}$ and ${\lambda }_{2}$, respectively are incident on a metallic surface. If ${\lambda }_{1}=3{\lambda }_{2}$ then :

The de Broglie wavelengths for an electron and a photon are ${\lambda }_{e}$ and ${\lambda }_{p}$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is ${v}_{1}$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes ${v}_{2}$. If ${v}_{2}=x{v}_{1}$, the value of $x$ will be _____ .

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its(i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

The electric field at a point associated with a light wave is given by $E=200[\mathrm{sin}(6\times {10}^{15})t+\mathrm{sin}(9\times {10}^{15})t]{\mathrm{Vm}}^{-1}$ Given: $h=4.14\times {10}^{-15}\mathrm{eVs}$ If this light falls on a metal surface having a work function of $2.50\mathrm{eV}$, the maximum kinetic energy of the photoelectrons will be

In a hydrogen spectrum $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "$a\lambda$" between the wavelength of ${3}^{\mathrm{rd}}$ transition line of Paschen series and that of ${2}^{\mathrm{nd}}$ transition line of Balmer Series where $a=$ _____.

Read the following statements: (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number. (C) Density of the nucleus is directly proportional to the mass number. (D) Density of the nucleus is directly proportional to the cube root of the mass number. (E) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

Given below are two statements Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit $({E}_{1})$ to higher energy orbit $({E}_{2})$, is given as $hf={E}_{1}-{E}_{2}$ Statement II: The jumping of electron from higher energy orbit $({E}_{2})$ to lower energy orbit $({E}_{1})$ is associated with frequency of radiation given as $f=\frac{({E}_{2}-{E}_{1})}{h}$. This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below:

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$. The value of principal quantum number $n$ of the excited state will be : ( $R:$ Rydberg constant)

The momentum of an electron revolving in ${n}^{th}$ orbit is given by : (Symbols have their usual meanings)

The ratio for the speed of the electron in the ${3}^{\mathrm{rd}}$ orbit of ${\mathrm{He}}^{+}$ to the speed of the electron in the ${3}^{\mathrm{rd}}$ orbit of hydrogen atom will be :

A hydrogen atom in its ground state absorbs $10.2\mathrm{eV}$ of energy. The angular momentum of electron of the hydrogen atom will increase by the value of (Given, Planck's constant $=6.6\times {10}^{-34}\mathrm{Js}$).

In Bohr's atomic model of hydrogen, let $K,P$ and $E$ are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

Mass numbers of two nuclei are in the ratio of $4:3$. Their nuclear densities will be in the ratio of

In the following nuclear reaction, $D\overset{\alpha }{\rightarrow }{D}_{1}\overset{{\beta }^{-}}{\rightarrow }{D}_{2}\overset{\alpha }{\rightarrow }{D}_{3}\overset{\gamma }{\rightarrow }{D}_{4}$ Mass number of $D$ is $182$ and atomic number is $74$ . Mass number and atomic number of ${D}_{4}$ respectively will be

A nucleus of mass $M$ at rest splits into two parts having masses $\frac{{M}^{'}}{3}$ and $\frac{2{M}^{'}}{3}({M}^{'}<M)$. The ratio of de Broglie wavelength of two parts will be

If the potential barrier across a $p-n$ junction is $0.6V$. Then the electric field intensity, in the depletion region having the width of $6\times {10}^{-6}m$, will be _____ $\times {10}^{5}N{C}^{-1}$

The energy band gap of semiconducting material to produce violet (wavelength $=4000Å$) LED is _____ $\mathrm{eV}$. (Round off to the nearest integer).

In the circuit, the logical value of $A=1$ or $B=1$ when potential at $A$ or $B$ is $5V$ and the logical value of $A=0$ or $B=0$ when potential at $A$ or $B$ is $0V$.  The truth table of the given circuit will be :

A potential barrier of $0.4V$ exists across a p-n junction. An electron enters the junction from the $n$-side with a speed of $6.0\times {10}^{5}{ms}^{-1}$. The speed with which electron enters the $p$ side will be $\frac{x}{3}\times {10}^{5}{ms}^{-1}$, then the value of $x$ is _____.: (Given mass of electron $=9\times {10}^{-31}\mathrm{kg}$, charge on electron $=1.6\times {10}^{-19}C$.)

The cut-off voltage of the diodes (shown in figure) in forward bias is $0.6V$. The current through the resister of $40\Omega$ is _____ $\mathrm{mA}$. 

Identify the correct Logic Gate for the following output $(Y)$ of two inputs $A$ and $B$. 

The $I-V$ characteristics of a $p-n$ junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of $2V$ and $4V$ respective is 

Identify the logic operation performed by the given circuit 

As per the given circuit, the value of current through the battery will be _____ A. 

An electron with speed $v$ and a photon with speed $c$ have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are ${E}_{e}$ and ${P}_{e}$ and that of photon are ${E}_{ph}$ and ${P}_{ph}$ respectively. Which of the following is correct?

A beam of monochromatic light is used to excite the electron in ${\mathrm{Li}}^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x\times {10}^{-10}m$. The value of $x$ is _____ . [Given $hc=1242\mathrm{eV}\mathrm{nm}$]

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between $A$ and $B$ is _____ $\Omega .$ 

A logic gate circuit has two inputs $A$ and $B$ and output $Y$. The voltage waveforms of $A,B$ and $Y$ are shown below  The logic gate circuit is

An electron (mass $m$) with an initial velocity $\vec{v}={v}_{0}\hat{i}({v}_{0}>0)$ is moving in an electric field $\vec{E}=-{E}_{0}\hat{i}({E}_{0}>0)$ where ${E}_{0}$ is constant. If at $t=0$, de-Broglie wavelength is ${\lambda }_{0}=\frac{h}{m{v}_{0}}$, then its de-Broglie wavelength after time $t$ is given by

The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be :

$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of $x$ will be

The $Q$-value of a nuclear reaction and kinetic energy of the projectile particle, ${K}_{p}$ are related as

Nucleus $A$ is having mass number $220$ and its binding energy per nucleon is $5.6\mathrm{MeV}$. It splits in two fragments $B$ and $C$ of mass numbers $105$ and $115$. The binding energy of nucleons in $B$ and $C$ is $6.4\mathrm{MeV}$ per nucleon. The energy $Q$ released per fission will be:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The photoelectric effect does not take place, if the energy of the incident radiation is less than the work function of a metal. Reason R : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.

Choose the correct option from the following options given below :

$\sqrt{{d}_{1}}$ and $\sqrt{{d}_{2}}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For ${d}_{1}=x{d}_{2}$, the value of $x$ will be _____ .

In the given circuit the input voltage ${V}_{\mathrm{in}}$ is shown in figure. The cut-in voltage of $p-n$ junction diode (${D}_{1}$ or ${D}_{2}$) is $0.6V$. Which of the following output voltage $({V}_{0})$ waveform across the diode is correct? 

Which of the following figure represents the variation of $\mathrm{ln}(\frac{R}{{R}_{0}})$ with $\mathrm{ln}A$ (if $R=$ radius of a nucleus and $A=$ its mass number)

A metal exposed to light of wavelength $800\mathrm{nm}$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $500\mathrm{nm}$ is used. The work function of the metal is (Take $hc=1230\mathrm{eV}-\mathrm{nm}$).

A $8V$ Zener diode along with a series resistance $R$ is connected across a $20V$ supply (as shown in the figure). If the maximum Zener current is $25\mathrm{mA}$, then the minimum value of $R$ will be _____ $\Omega$. 

In the given circuit, the value of current ${I}_{L}$ will be _____ $\mathrm{mA}.$ (When ${R}_{L}=1k\Omega$) 

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $6630Å$ is $0.42V$. If the threshold frequency is $x\times {10}^{13}s$, where $x$ is (nearest integer): (Given, speed light $=3\times {10}^{8}m{s}^{-1}$. Planck's constant $=6.63\times {10}^{-34}Js$)

A Zener of breakdown voltage ${V}_{Z}=8V$ and maximum Zener current, ${I}_{\mathrm{ZM}}=10\mathrm{mA}$ is subjected to an input voltage ${V}_{i}=10V$ with series resistance $R=100\Omega$. In the given circuit ${R}_{L}$ represents the variable load resistance. The ratio of maximum and minimum value of ${R}_{L}$ is _____ . 

The equation $\lambda =\frac{1.227}{x}\mathrm{nm}$ can be used to find the de-Broglie wavelength of an electron. In this equation $x$ stands for : Where, $m=$ mass of electron $P=$ momentum of electron $K=$ Kinetic energy of electron $V=$ Accelerating potential in volts for electron

Identify the solar cell characteristics from the following options :

An $\alpha$ particle and a carbon $12$ atom has same kinetic energy $K$. The ratio of their de-Broglie wavelengths $({\lambda }_{\alpha }:{\lambda }_{C12})$ is

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode

In the circuit shown below, maximum Zener diode current will be _____ $\mathrm{mA}$. 

The light of two different frequencies whose photons have energies $3.8\mathrm{eV}$ and $1.4\mathrm{eV}$ respectively, illuminate a metallic surface whose work function is $0.6\mathrm{eV}$ successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :

With reference to the observations in photo-electric effect, identify the correct statements from below: A. The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. B. The value of saturation current increases on moving the source of light away from the metal surface. C. The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. D. The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. E. Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below:

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: $X12+X12=Y24$ The binding energies per nucleon $X12$ and $Y24$ are $1.1\mathrm{MeV}$ and $7.6\mathrm{MeV}$ respectively. The energy released in this process is_____ $\mathrm{MeV}$.