Modern Physics — JEE Main PYQs

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B , which in turn disintegrates to some other stable nucleus C . Plot of a graph showing the variation of number of atoms of nucleus $B$ vesus time is :
(Assume that at $t=0$, there are no $B$ …

If '$f$' denotes the ratio of the number of nuclei decayed ($N_d$) to the number of nuclei at $t=0$ ($N_0$) then for a collection of radioactive nuclei, the rate of change of '$f$' with respect to time is given as: [$\lambda$ is the radioactive decay constant]

A particle of mass $9.1\times 10^{-31}\mathrm{kg}$ travels in a medium with a speed of $10^6\mathrm{m}/\mathrm{s}$ and a photon of a radiation of linear momentum $10^{-27}\mathrm{kg}\mathrm{m}/\mathrm{s}$ travels in vacuum. The wavelength of photon is ______ times the wavelength of …

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5\mathring{A}$. If the speed of electron is $2.2\times 10^6\mathrm{m}/\mathrm{s}$, then the current associated with the electron will be $\simeq$ ______ $\times 10^{-2}\mathrm{mA}$. [Take $\pi$ …

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance $200\mu \mathrm{F}$ is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then …

An electron of mass $m$ and a photon have same energy $E$. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

If an electron is moving in the ${\mathrm{n}}^{\text{th }}$ orbit of the hydrogen atom, then its velocity $\left(v_{\mathrm{n}}\right)$ for the ${\mathrm{n}}^{\text{th }}$ orbit is given as :

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where $\lambda$ is the decay constant)

What should be the order of arrangement of de-Broglie wavelength of electron (${\lambda }_{\mathrm{e}}$), an $\alpha$-particle $({\lambda }_{\alpha })$ and proton $({\lambda }_{\mathrm{p}})$ given that all have the same kinetic energy?

The half-life of ${}^{198}\mathrm{Au}$ is 3 days. If atomic weight of ${}^{198}\mathrm{Au}$ is $198\mathrm{g}/\mathrm{mol}$ then the activity of 2 mg of ${}^{198}\mathrm{Au}$ is [ in disintegration/ second ] :

A particle of mass 4 M at rest disintegrates into two particles of mass M and 3 M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3 M will be :

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelen …

From the given data, the amount of energy required to break the nucleus of aluminium ${}_{13}^{27}\mathrm{Al}$ is $x\times 10^{-3}$ J.
Mass of neutron $=1.00866$ u
Mass of proton $=1.00726$ u
Mass of Aluminium nucleus $=27.18846$ u
(Assume 1 u corresponds to xJ of energy)
(Round o …

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$, with maximum kinetic energy are bent into circular arc of radius 30 cm. The value …

The nuclear activity of a radioactive element becomes ${\left(\frac{1}{8}\right)}^{\text{th }}$ of its initial value in 30 years. The half-life of radioactive element is ____ years.

Consider the following statements:
(A) Atoms of each element emit characteristics spectrum.
(B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
(C) The density of nuclear matter depends on the size of the nucleus.
(D) A free …

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavel …

The ${\mathrm{K}}_{\alpha }$-X ray of molybdenum has wavelength 0.071 nm . If the energy of a molybdenum atom with a K electron knocked out is 27.5 keV , the energy of this atom when an L electron is knocked out will be ____ ke V. (Round off to the nearest integer) …

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then:

The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is:
[$\mathrm{me}=$ mass of electron $=9\times 10^{-31}\mathrm{kg}$
$\mathrm{h}=$ Planck constant $=6.6\times 10^{-34}\mathrm{Js}$ …

The stopping potential in the context of photoelectric depends on the following property of incident electromagnetic radiation:

The first three spectral of H -atom in the Balmer series are given ${\lambda }_1,{\lambda }_2,{\lambda }_3$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{{\lambda }_1}{{\lambda }_3}\right)$ are related by a factor of approxima …

Calculate the time interval between $33\%$ decay and $67\%$ decay if half-life of a substance is 20 minutes.

The half- life of ${\mathrm{Au}}^{198}$ is 2.7 days. The activity of $1.50{\mathrm{mg}}^{198}$ of ${\mathrm{Au}}^{198}$ if atomic weight is $198\mathrm{g}{\mathrm{mol}}^{-1}$ is, $\left({\mathrm{N}}_{\mathrm{A}}=6\times 10^{23}/\mathrm{mol}\right)$

The de - Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V . What should be the ratio of their wavelengths? …

The speed of electrons in a scanning electron microscope is $1\times 10^7\mathrm{m}/\mathrm{s}$. If protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of

The decay of a proton to neutron is :

Two identical photo-cathodes receive the light of frequencies $f_1$ and $f_2$ respectively. If the velocities of the photo-electrons coming out are $v_1$ and $v_2$ respectively, then

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A particle of mass $m$ moves in a circular orbit in a central potential field $U(r)=U_0{r}^4$. If quantization conditions are applied, radii of possible orbitals $r_n$ vary with $n^{\frac{1}{\alpha }}$, where $\alpha$ is ______

A radioactive sample disintegrates via two independent decay processes having half lives ${\mathrm{T}}_{1/2}^{(1)}$ and ${\mathrm{T}}_{1/2}^{(2)}$ respectively. The effective half-life, ${\mathrm{T}}_{1/2}$ of the nuclei is :

Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu )$. The mass of muon particle is 207 times that of an electron and charge is equal to the charge is of an electron. The ionization potential of this hydrogen atom will be :

A particle is traveling 4 times as fast as an electron. Assuming the ratio of de- Broglie wavelength of a particle to that of electron is $2:1$, the mass of the particle is :

The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6\times 10^{-16}\text{s}$. The frequency of revolution of the electron in its first excited state (in ${\text{s}}^{-1}$) is

A beam of electromagnetic radiation of intensity $6.4\times 10^{-5}\mathrm{W}/{\mathrm{cm}}^2$ is comprised of wavelength, $\lambda =310\mathrm{nm}$. It falls normally on a metal (work function $\phi =2\mathrm{eV}$ ) of surface area $1{\mathrm{cm}}^2$. If one i …

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ($c=$ speed of light in vacuum)

The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$ in 30 minutes. Its half life is close to

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${\mathrm{T}}_{\mathrm{A}}\mathrm{eV}$ and de-Broglie wavelength ${\lambda }_{\mathrm{A}}$. The maximum kinetic energy of photoelectrons liberated form another metal …

The graph which depicts the results of Rutherford gold foil experiment with $\alpha$-particles is
$\theta$ : Scattering angle
Y : Number of scattered $\alpha$-particles detected
(Plots are schematic and not to scale)

An electron (mass $m$) with initial velocity $\vec{v}=v_0\hat{i}+v_0\hat{j}$ is in an electric field $\vec{E}=-E_0\hat{k}$. If ${\lambda }_0$ is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time $t$ is given by

The first member of the Balmer series of hydrogen atom has a wavelength of $6561\mathring{A}$. The wavelength of the second member of the Balmer series (in nm) is ____.

The energy required to ionize a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state?

An electron of mass $m$ and magnitude of charge $|e|$ initially at rest gets accelerated by a constant electric field E . The rate of change of de-Broglie wavelength of this electron at time $t$ ignoring relativistic effects is

Radiation, with wavelength $6561\text{ A˚}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3\times 10^{-4}\text{ T}$. If the radius of the largest circular path followed by the electrons is 10 mm, the work functi …

A particle moving with kinetic energy E has de Broglie wavelength $\lambda$. If energy $\Delta \mathrm{E}$;is added to its energy, the wavelength become $\lambda /2$. Value of $\Delta \mathrm{E}$, is:

A radioactive nucleus decays by two difference processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is closes to:

The surface of a metal is illuminated alternately with photons of energies ${\mathrm{E}}_1=4\mathrm{eV}$ and ${\mathrm{E}}_2=2.5\mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is …

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to: