Modern Physics — JEE Main PYQs

If the series limit frequency of the Lyman series is ${\nu }_L$, then the series limit frequency of the Pfund series is:

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If ${\lambda }_{\text{min }}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of …

A radioactive nucleus A with a half life T, decays into a nucleus B. At $t=0$, there is no nucleus B. At sometime $t$, the ratio of the number of B to that of A is 0.3. Then, $t$ is given by :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by:

A particle A of mass $m$ and initial velocity $v$ collides with a particle B of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda }_A$ to ${\lambda }_B$ after the collision is:

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :
A : Blue light
B : Yellow light
C : X-ray
D : Radiowave

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 emitted electron will be :

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list:

Hydrogen $\left({}_1{\mathrm{H}}^1\right)$, Deuterium $\left({}_1{\mathrm{H}}^2\right)$, singly ionised Helium ${\left({}_2{\mathrm{He}}^4\right)}^{+}$ and doubly ionised lithium ${\left({}_3{\mathrm{Li}}^6\right)}^{++}$ all have one electron around the nucleus. Consider an e …

The radiation corresponding to $3\to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times 10^{-4}\mathrm{T}$. If the radius of the largest circular path followed by these elec …

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number ( $\mathrm{n}-1$ ). If $\mathrm{n}\gg 1$, the frequency of radiation emitted is proportional to

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements

Statement 1: Davisson - germer experiment established the wave nature of electrons.

Statement 2: If electrons have wave nature, t …

Assume that a neutron breaks into a proton and an electron. The energy released during this process is (Mass of neutron $=1.6725\times 10^{-27}$ kg; mass of proton $=1.6725\times 10^{-27}$ kg; mass of electron $=9\times 10^{-31}$ kg)

A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( n is an integer)

Energy required for the electron excitation in ${\mathrm{Li}}^{++}$ from the first to the third Bohr orbit is :

The half life of a radioactive substance is 20 minutes. The approximate time interval $(t_2-t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ and $\frac{1}{3}$ of it had decayed is :

This question has Statement -1 and Statement -2 . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency $\mathrm{v}>{\mathrm{v}}_0$ (the threshold …

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is ${\mathrm{V}}_0$ and the maximum kinetic energy of the photoelectrons is ${\mathrm{K}}_{\max }$. When the ultraviolet light is replaced by X rays, both ${\mathrm{V}}_0$ and …

The binding energy per nucleon for the parent nucleus is ${\mathrm{E}}_1$ and that for the daughter nuclei is ${\mathrm{E}}_2$. Then

The speed of daughter nuclei is

A radioactive nucleus (initial mass number A and atomic number Z ) emits $3\alpha$-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

If a source of power 4 kW produces $10^{20}$ photons/second, the radiation belong to a part of the spectrum called

The above is a plot of binding energy per nucleon ${\mathrm{E}}_{\mathrm{b}}$, against the nuclear mass $\mathrm{M};\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E},\mathrm{F}$ correspond to different nuclei. Consider four reactions:
(i) …

The transition from the state $\mathrm{n}=4$ to $\mathrm{n}=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc $=1240\mathrm{eV}\mathrm{nm}$)

Electrons accelerated by potential V are diffracted from a crystal. If $\mathrm{d}=1\mathring{A}$ and $\mathrm{i}=30^{\circ },\mathrm{V}$ should be about ( …

If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance 'd' between them (see figure), de Broglie wavelength ${\lambda }_{\mathrm{dB}}$ of electrons can be calculated by the relationship (n is an inte …

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - I:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
and
Statement - II
For h …

Suppose an electron is attracted towards the origin by a force $\mathrm{k}/\mathrm{r}$ where ' k ' is a constant and ' r ' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the ${\mathrm{n}}^{\text{th }}$ orbital of the ele …

If $M_O$ is the mass of an oxygen isotope ${}_8{O}^{17}$, $M_p$ and $M_N$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

In gamma ray emission from a nucleus

Photon of frequency $\nu$ has a momentum associated with it. If c is the velocity of light, the momentum is

The half-life period of a radioactive element X is the same as the mean-life time of another radioactive element Y. Initially they have the same number of atoms. Then

The time by a photoelectron to come out after the photon strikes is approximately

The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV, and the stopping potential for a radiation incident on this surface 5 V. The incident radiation lies in

The energy spectrum of $\beta$-particles [number $\mathrm{N}(\mathrm{E})$ as a function of $\beta$-energy E] emitted from a radioactive source is

When ${}_3{\mathrm{Li}}^7$ nuclei are bombarded by protons, and the resultant nuclei are ${}_4{\mathrm{Be}}^8$, the emitted particles will be

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows :

The 'rad' is the correct unit used to report the measurement of

If the binding energy per nucleon in ${}_3^7\mathrm{Li}$ and ${}_2^4\mathrm{He}$ nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction
$\mathrm{p}+{}_3^7\mathrm{Li}\to 2{}_2^4\mathrm{He}$
energy of proton must be

The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to $\frac{1}{8}$. The thickness of lead which will reduce the intensity to $\frac{1}{2}$ will be

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap in (eV) for the semiconductor is

A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed $\frac{1}{2}\mathrm{m}$ away, the number of electrons emitted by photo cathode would

Starting with a sample of pure ${}^{66}\mathrm{Cu}$, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is

If radius of ${}_{13}^{27}\mathrm{Al}$ nucleus is estimated to be 3.6 Fermi then the radius ${}_{52}^{125}\mathrm{Te}$ nucleus be nearly