Modern Physics — JEE Main PYQs

In a radioactive material, fraction of active material remaining after time $t$ is $9/16$. The fraction that was remaining after $t/2$ is

Two sources of light emit X - rays of wavelength 1 nm and visible light of wavelength 500 nm , respectively. Both the sources emit light of the same power 200 W . The ratio of the number density of photons of X- rays to the number density of photons of the visible light of the gi …

If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm , then its band gap energy is:
Planck's constant $\mathrm{h}=6.63\times 10^{-34}\mathrm{J}.\mathrm{s}$.
Speed of light $c=3\times 10^8\mathrm{m}/\mathrm{s}$

The radius R of a nucleus of mass number A can be estimated by the formula $R=\left(1.3\times 10^{-15}\right)A^{1/3}\mathrm{m}$. It follows that the mass density of a nucleus is of the order of: …

Given the masses of various atomic particles $m_p=1.0072u,m_n=1.0087u,m_e=0.000548\mathrm{u},{\mathrm{m}}_{\mathrm{v}}^{-}=0,{\mathrm{m}}_{\mathrm{d}}=2.0141\mathrm{u}$, where $\mathrm{p}\equiv$ proton, $\mathrm{n}\equiv$ neutron, $\mathrm{e}\equiv$ electron, …

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to:
(Given: nitrogen molecule weight: $4.64\times 10^{-26}$ kg, Boltzman constant: $1.38\times 10^{-23}$ J/K, Planck constant: $6.63\times 10^{-34}$ …

With increasing biasing voltage of a photodiode, the photocurrent magnitude:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives $T_{\frac{1}{2}}(A):T_{\frac{1}{2}}(B):T_{\frac{1}{2}}(C)$ are in the ratio:

A particle of mass $200$ MeV$/c^2$ collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is $\frac{N}{4}$. The value of N is: (Given …

A beam of electrons of energy $E$ scatters from a target having atomic spacing of $1$ Å. The first maximum intensity occurs at $\theta =60^{\circ }$. Then $E$ (in eV) is ______.
(Planck constant $h=6.63\times 10^{-34}$ J·s, electron mass $m=9.1\times 10^{-31}$ kg)

An electron, a doubly ionized helium ion $\left({\mathrm{He}}^{++}\right)$ and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength ${\lambda }_{\mathrm{e}},{\lambda }_{\mathrm{He}}++$ and ${\lambda }_{\mathrm{p}}$ is:

You are given that Mass of ${}_3^7\mathrm{Li}=7.0160\mathrm{u}$, Mass of ${}_2^4\mathrm{He}=4.0026\mathrm{u}$ and ${}_1^1\mathrm{H}=1.0079\mathrm{u}$. When 20 g of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton captu …

Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Plancks constant $\mathrm{h}=6.62\times 10^{-34}$ J.s)

Particle A of mass ${\mathrm{m}}_{\mathrm{A}}=\frac{\mathrm{m}}{2}$ moving along the x-axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$. If both particles move along the $x$ axis after the collision, the change …

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is $304\text{A˚}$. The corresponding difference for the Paschan series in Å is: ____.

In photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased:

Find the binding energy per nucleon for ${}_{50}^{120}\mathrm{Sn}$. Mass of proton ${\mathrm{m}}_{\mathrm{p}}=1.00783\mathrm{U}$, mass of neutron $m_n=1.00867\mathrm{U}$ and mass of tin nucleus $m_{\mathrm{Sn}}=119.902199\mathrm{U}$. (take $1\mathrm{U}=931\mathrm{MeV}$)

Two particles move at right angle to each other. Their de Broglie wavelengths are ${\lambda }_1$ and ${\lambda }_2$ respectively. The particles suffere perfectly inelastic collision. The de Broglie wavelength $\lambda$, of the final particle, is given by:

Radiation coming from transition $\mathrm{n}=2$ to $\mathrm{n}=1$ of hydrogen atoms fall of ${\mathrm{He}}^{+}$ions in $\mathrm{n}=$ 1 and $\mathrm{n}=2$ states. The possible. Transition of helium ions as they absorb energy from the radiation is:

The ratio of mass densities of nuclei of ${}^{40}Ca$ and ${}^{16}O$ is close to:

A nucleus A, with a finite de-broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavele …

The electric field of light wave is given as $\vec{E}=10^{-3}\cos \left(\frac{2\pi x}{5\times 10^{-7}}-2\pi \times 6\times 10^{14}t\right)\hat{x}\frac{N}{C}$. This light falls on a metal plate of work function 2 eV . The stopping potential of the photoelectrons is:

Taking the wavelength of first Balmer line in hydrogen spectrum ( $\mathrm{n}=3$ to $\mathrm{n}=2$ ) as 660 nm , the wavelength of the $2^{\text{nd }}$ Balmer line ( $\mathrm{n}=4$ to $\mathrm{n}=2$ ) will be

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of $7.5\times 10^{-12}\mathrm{m}$, the minimum electron energy required is close to:

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t=0$ it was 1600 counts per second and $t=8$ seconds it was 100 counts per second. The count rate observed, as counts per second, at $\mathrm{t}=6$ seconds is close to:

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell the wavelength of emitted radiation is $\lambda$. If an electron jumps from N-shell to the L-shell the wavelength of emitted radiation will be:

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to $\left(\frac{\mathrm{hc}}{\mathrm{e}}=1240\mathrm{nm}-\mathrm{V}\right)$

The stopping potential ${\mathrm{V}}_0$ (in volt) as a function of frequency ( $v$ ) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be :
(Given : Planck's constant …

An excited ${\mathrm{He}}^{+}$ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm , in making a transition to ground state. The quantum number n , corresponding to its initial excited state is (for photon of wavelength $\lambda$, energy …

Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At $\mathrm{t}=0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\left(\frac{1}{\mathrm{e}}\right)}^2$ will be

In ${\mathrm{Li}}^{++}$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. When the ion gets deexcited to the ground state in all possible ways(including intermediate emission) a total of six spectral lines are observed. What is the value of …

A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is
[Given Planck's constant $\mathrm{h}=6.6\times 10^{-34}\mathrm{Js}$, speed of light $\mathrm{c}=3.0\times 10^8\mathrm{m}/\mathrm{s}$]

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980\mathring{A}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be:
($hc=12500\mathrm{eV}$ - Å)

If the deBroglie wavelength of an electron is equal to $10^{-3}$ times the wavelength of a photon of frequency $6\times 10^{14}\mathrm{Hz}$, then the speed of electron is equal to: (Speed of light = $3\times 10^8\mathrm{m}/\mathrm{s}$; Planck's constant …

A particle of mass $m$ moves in a circular orbit in a central potential field $U(r)=\frac{1}{2}k{r}^2$. If Bohr's quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number n as:

A particle $A$ of mass ' $m$ ' and charge ' $q$ ' is accelerated by a potential difference of 50 V . Another particle B of mass ' 4 m ' and charge ' q ' is accelerated by a potential difference of 2500 V . The ratio of de-Broglie wavelength …

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $4.65\mathring{A}$). The de-Broglie wavelength of this electron is :

Half lives of two radioactive nuclei $A$ and $B$ are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei $A$ and $B$ will be :

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${\lambda }_1/{\lambda }_2$, of the photons emitted in this process is:

In a Frank-hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}\mathrm{Th}$. At the end there are $6\alpha$ particles and $4\beta$-particles which are emitted. If the end nucleus is ${}_Z^{A}X,A$ and $Z$ are given by :

When a certain photosensitive surface is illuminated with monochromatic light of frequency v , the stopping potential for the photo current is $-{\mathrm{V}}_0/2$. When the surface is illuminated by monochromatic light of frequency $\mathrm{v}/2$, the stopping potential is …

A He${}^{+}$ ion is in its first excited state. Its ionization energy is:

At a given instant, say $t=0$, two radioactive substances $A$ and $B$ have equal activites. The ratio $\frac{R_B}{R_A}$ of their activities after time $t$ itself decays with time $t$ as $e^{-3t}$. If the half-life of $A$ is $\ell n2$, the half-life of $B$ is:

The magnetic field associated with a light wave is given, at the origin, by


If this light falls on a silver plate having a work function of …

Surface of certain metal is first illuminated with light of wavelength ${\lambda }_1=350\mathrm{nm}$ and then, the light of wavelength ${\lambda }_2=540\mathrm{nm}$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work …

A sample of radioactive material A , that has an activity of $10\mathrm{mCi}(1\mathrm{Ci}=3.7\times 10^{10}$ decays/s), has twice the number of nuclei as another sample of different radioactive material B which has an activity of 20 mCi . The correct choices for …

Two radioactive materials A and B have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time:

In a photoelectric effect experiment the threshold wavelength of the metal is 380 nm. If the wavelength of the incident light is 260 nm, the maximum kinetic energy of the emitted electrons will be: Given E (in eV) $=\frac{1237}{\lambda (\mathrm{in}\mathrm{nm})}$

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda }_n$, ${\lambda }_g$ be the de Broglie wavelength of the electron in the $n^{\text{th}}$ state and the ground state respectively. Let ${\Lambda }_n$ be the wavelength of the …