Modern Physics — JEE Main PYQs

7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.
[$\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ Nm²/C² and electron charge $=1.6\times 10^{-19}$ C]

The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $=1.66\times 10^{-27}$ kg, $h=6.6\times 10^{-34}$ J.s and $c=3\times 10^8$ m/s]

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $\_\_\_\_$ nm.

Light is incident on a metallic plate having work function $110\times 10^{-20}\mathrm{J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $\mathrm{rad}/\mathrm{s}$. ( …

The energy of an electron in an orbit of the Bohr's atom is $-0.04{\mathrm{E}}_0\mathrm{eV}$ where ${\mathrm{E}}_0$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …

A particle having electric charge $3\times 10^{-19}\mathrm{C}$ and mass $6\times 10^{-27}\mathrm{kg}$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $\alpha \times 10^{-12}\mathrm{m}$. The va …

The de Broglie wavelength of an oxygen molecule at $27^{\circ }\text{C}$ is $x\times 10^{-12}\text{ m}$. The value of x is (take Planck's constant $=6.63\times 10^{-34}\text{ J⋅s}$, Boltzmann constant $=1.38\times 10^{-23}\text{ J/K}$, mass of oxygen molecule …

In hydrogen atom spectrum, (R → Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is $\frac{4}{3R}$
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$
D. the m …

Which of the following pair of nuclei are isobars of the element?

The average energy released per fission for the nucleus of ${}_{92}^{235}\mathrm{U}$ is 190 MeV. When all the atoms of 47 g pure ${}_{92}^{235}\mathrm{U}$ undergo fission process, the energy released is $\alpha \times 10^{23}$ MeV. The value of $\alpha$ is $\_\_\_\_$.
(Avogadro Numbe …

Two electrons are moving in orbits of two hydrogen like atoms with speeds $3\times 10^5\mathrm{m}/\mathrm{s}$ and $2.5\times 10^5\mathrm{m}/\mathrm{s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ res …

Given below are two statements:

Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.

Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. …

An atom ${}_3^{8}X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by:

The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n:1$. The value of $n$ is ____.
(Assume mass of proton $=$ mass of neutron)

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V. The wavelength of first light is ____ m.
(h = 6.63 × 10⁻³⁴ J …

The binding energy for the following nuclear reactions are expressed in MeV.
${}_{2}H{e}^3{+}_0{n}^1{\to }_{2}H{e}^4+20$ MeV
${}_{2}H{e}^4{+}_0{n}^1{\to }_{2}H{e}^5-0.9$ MeV
If X₃, X₄, X₅ denote the stability of ${}_{2}H{e}^3$, ${}_{2}H{e}^4$ and …

A nucleus has mass number $\alpha$ and radius $R_{\alpha }$. Another nucleus has mass number $\beta$ and radius ${\mathrm{R}}_{\beta }$. If $\beta =8\alpha$ then $R_{\alpha }/R_{\beta }$ is :

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ______.
(Given : $\mathrm{h}=6.63\times 10^{-34}$ J.s and $\mathrm{c}=3\times 10^8\mathrm{m}/\mathrm{s}$ )

A light wave described by $\mathrm{E}=60\sin \left(3\times 10^{15}\right)\mathrm{t}+\sin \left(12\times 10^{15}\right)$ t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately)
____ eV. …

The binding energy per nucleon of ${}_{83}^{209}\mathrm{Bi}$ is $\_\_\_\_$ MeV.
[Take $\mathrm{m}\left({}_{83}^{209}\mathrm{Bi}\right)=208.980388\mathrm{u}$, ${\mathrm{m}}_{\mathrm{p}}=1.007825\mathrm{u}$, ${\mathrm{m}}_{\mathrm{n}}=1.008665\mathrm{u}$, …

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom.

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass number 3, 4 and 10 are $5.6$ MeV, $7.4$ MeV and $6.1$ MeV, respectively, then in the process, $\Delta M{c}^2=$ ______ Me …

The graph shows variation of stopping potential $V_o$ 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?

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
(A)The size of gold nucleus is very small as compared to the size of gold atom.
(B) Alpha particle and gold nucleus have equal charge.
(C) The impact parameter is minimum for a f …

The de Broglie wavelength associated with an electron accelerated through a potential difference V is ${\lambda }_{\mathrm{e}}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is ${\lambda }_{\mathrm{p}}$. If their corresponding …

An electron of mass $m$ is moving in an electric field $\overrightarrow{\mathrm{E}}=-2{\mathrm{E}}_0\hat{\mathrm{i}}$ (${\mathrm{E}}_0=$ constant $>0$), with an initial velocity $\overrightarrow{\mathrm{V}}={\mathrm{v}}_{\mathrm{o}}\hat{\mathrm{i}}$ (${\mathrm{v}}_0=$ constant …

In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The ratio of the radius of the orbits in given by ${\mathrm{r}}_{\mathrm{i}}:{\mathrm{r}}_f=16:4$. The wavelength of photon emitted due to this transition is ______ nm. (Given Ry …

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, …

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 va …

Assuming the experimental mass of ${}_6^{12}\mathrm{C}$ as 12 u, the mass defect of ${}_6^{12}\mathrm{C}$ atom is ______ $\mathrm{MeV}/{\mathrm{c}}^2$. (Mass of proton $=1.00727\mathrm{u}$. mass of neutron …

The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha /\beta$. The possible values of $\alpha$ and $\beta$ are :-

The energy released when $\frac{7}{17.13}\mathrm{kg}$ of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton bombardment is $\alpha \times 10^{32}\mathrm{eV}$. The value of $\alpha$ is $\_\_\_\_$. (Nearest integer)
(Mass of …

The energy released if hydrogen atoms are combined to form $\frac{4}{2}\mathrm{He}$ is ______.
(Take binding energies per nucleon of ${}_1^2\mathrm{H}$ and ${}_2^4\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively).

The de Broglie wavelength for an electron accelerated through the potential difference $V_1$ volt is ${\lambda }_1$. When the potential difference is changed to ${\mathrm{V}}_2$ volt, the associated de Broglie wavelength is increased by $50\%$. If …

A monochromatic source of light operating at 15 kW emits $2.5\times 10^{22}$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ______.
(Take $\mathrm{h}=6.6\times 10^{-34}\mathrm{J}$.s and …

${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ 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 …

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same Q value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and $B$ is ______.

For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3{\mathrm{V}}_0$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potential becomes ${\mathrm{V}}_0$. The th …

Angular momentum of an electron in a hydrogen atom is $\frac{3\mathrm{h}}{\pi }$, then the energy of the electron is ____ eV.

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times 10^{-11}\mathrm{m}$ while that for the electron in third excited state is $8.48\times 10^{-10}\mathrm{m}$. The ratio of the de Broglie wavelengths of electron in the ground state to th …

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 surface, then photo-electric effect is possible for the case of

A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength $\frac{\lambda }{2}$, then the maximum kinetic energy of ejected electrons will be …

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

A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus ${\mathrm{n}}_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of ${\mathrm{n}}_2$ to the number of nuclei of …

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 2 V , what is the wavelength of the em-wave?
(Given hc $=1242\mathrm{eVnm}$ where h is the Planck' …

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.
Reason (R) : Nu …

In an experiment with photoelectric effect, the stopping potential.

The number of spectral lines emitted by atomic hydrogen that is in the $4^{\text{th}}$ energy level, is

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
Reason …

If $\lambda$ and K are de Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be :-