Modern Physics — JEE Main PYQs

A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns . Assuming speed of light as $3\times 10^8\mathrm{m}/\mathrm{s}$. the momentum of the object becomes equal to :

Speed of an electron in Bohr's $7^{\text{th }}$ orbit for Hydrogen atom is $3.6\times 10^6\mathrm{m}/\mathrm{s}$. The corresponding speed of the electron in $3^{\text{rd }}$ orbit, in $\mathrm{m}/\mathrm{s}$ is :

If a source of electromagnetic radiation having power 15 kW produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is.
(Take Planck constant $\mathrm{h}=6\times 10^{-34}$ Js)

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Given below are two statements: One is labelled as
Assertion A and the other is labelled as Reason R
Assertion A: The beam of electrons shows wave nature and exhibit interference and diffraction.
Reason R : Davisson Germer Experimentally verified the wave nature of electrons.
In …

For hydrogen atom, ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ${\lambda }_1$ and ${\lambda }_2$ is $\frac{x}{32}$. The value of $x$ is $\_\_\_\_$.

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

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

If the binding energy of ground state electron in a hydrogen atom is 13.6 eV, then, the energy required to remove the electron from the second excited state of ${\mathrm{Li}}^{2+}$ will be: $x\times 10^{-1}$ eV. The value of $x$ is ____.

An electron of a hydrogen like atom, having $Z=4$, jumps from $4^{\text{th}}$ energy state to $2^{\text{nd}}$ energy state. The energy released in this process, will be:
(Given Rch $=13.6\text{eV}$)
Where $R=$ Rydberg constant
$c=$ Speed of light in vacuum
h = Planck's constant

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 …

Nucleus A having $Z=17$ and equal number of protons and neutrons has 1.2 MeV binding energy per nucleon.
Another nucleus B of $Z=12$ has total 26 nucleons and 1.8 MeV binding energy per nucleons.
The difference of binding energy of B and A will be ______ MeV.

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 proportion …

Two radioactive materials A and B have decay constants $25\lambda$ and $16\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $\frac{1}{a\lambda }$. The value of a is ______.

The equation $\lambda =\frac{1.227}{\mathrm{x}}\mathrm{nm}$ can be used to find the de-Brogli wavelength of an electron. In this equation x stands for :

Where,
$\mathrm{m}=$ mass of electron
$\mathrm{P}=$ momentum of electron
K=Kinetic energy of electron
$\mathrm{V}=$ Ac …

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$ th of its original mass to disintegrate will be :

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be ____ hours.

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

A radioactive sample decays to $\frac{1}{8}$th of its original quantity in 15 minutes. The half-life of the sample is

An electron (mass m) with an initial velocity $\overrightarrow{\mathrm{v}}={\mathrm{v}}_0\hat{\mathrm{i}}$ (${\mathrm{v}}_0>0$) is moving in an electric field $\overrightarrow{\mathrm{E}}=-{\mathrm{E}}_0\hat{\mathrm{i}}$ (${\mathrm{E}}_0>0$) where ${\mathrm{E}}_0$ is …

What is the half-life period of a radioactive material if its activity drops to $1/16^{\text{th }}$ of its initial value of 30 years?

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

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

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

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

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

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
${}_1^2\mathrm{X}+{}_1^2\mathrm{X}={}_2^4\mathrm{Y}$
The binding energies per nucleon ${}_1^2\mathrm{X}$ and ${}_2^4\mathrm{Y}$ are 1.1 MeV and 7.6 MeV respect …

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 ligh …

The activity of a radioactive material is $6.4\times 10^{-4}$ curie. Its half life is 5 days. The activity will become $5\times 10^{-6}$ curie after:

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

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)

$\frac{x}{x+4}$ 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 disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :
(Take ${\log }_{10}1.88=0.274$)

A parallel beam of light of wavelength 900 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 :

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 $3^{\text{rd}}$ transition line of Paschen series and that of $2^{\text{nd}}$ transition line of Balmer S …

Let ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ 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:

Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of th …

Given below are two statements:

Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit ( ${\mathrm{E}}_1$ ) to higher energy orbit ( ${\mathrm{E}}_2$ ), is given as $\mathrm{hf}={\mathrm{E}}_1-{\mathrm{E}}_2$.

Statement- …

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?

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, $K_p$ are related as:

In the following nuclear reaction,
$\mathrm{D}\stackrel{\alpha }{\to }{\mathrm{D}}_1\stackrel{{\beta }^{-}}{\to }{\mathrm{D}}_2\stackrel{\alpha }{\to }{\mathrm{D}}_3\stackrel{\gamma }{\to }{\mathrm{D}}_4$
Mass number of D is 182 and atomic number is 74. Mass number and atomic number of …

The electric field at the point associated with a light wave is given by
$\mathrm{E}=200\left[\sin \left(6\times 10^{15}\right)\mathrm{t}+\sin \left(9\times 10^{15}\right)\mathrm{t}\right]{\mathrm{Vm}}^{-1}$
Given: $\mathrm{h}=4.14\times 10^{-15}\mathrm{eVs}$
If this light fal …

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to $6.25\%$ of its initial value. The value of x is ______.

A metal surface is illuminated by a radiation of wavelength $4500\mathring{A}$. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of $90^{\circ }$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of …

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be :

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

The activity of a radioactive material is $2.56\times 10^{-3}$ Ci. If the half life of the material is 5 days, after how many days the activity will become $2\times 10^{-5}\mathrm{Ci}$?

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 phot …

$\sqrt{d_1}$ 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 ____.

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 ${\mathrm{E}}_{\mathrm{e}}$ and ${\mathrm{p}}_{\mathrm{e}}$ and that of photon are ${\mathrm{E}}_{\mathrm{ph}}$ and ${\mathrm{p}}_{\mathrm{ph}}$ resp …