Modern Physics — JEE Main PYQs

Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x}\times 10^{-10}$ m. The value of the $x$ is ____.
($1\text{ eV}=1.6\times 10^{-19}$ J, …

The half-life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$ th part of its original mass will be :

The variation of stopping potential (${\mathrm{V}}_0$) as a function of the frequency ($v$) of the incident light for a metal is shown in figure. The work function of the surface is

If $917\mathring{A}$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ____ Å.

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be:

The de Broglie wavelength of a molecule in a gas at room temperature ( 300 K ) is ${\lambda }_1$. If the temperature of the gas is increased to 600 K , then the de Broglie wavelength of the same gas molecule becomes

The decay constant for a radioactive nuclide is $1.5\times 10^{-5}{\mathrm{s}}^{-1}$. Atomic mass of the substance is 60 g mole${}^{-1}$, $({\mathrm{N}}_{\mathrm{A}}=6\times 10^{23})$. The activity of $1.0\mu \mathrm{g}$ of the substance is $\_\_\_\_$ $\times 10^{10}\mathrm{Bq}$.

A metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is ${\mathrm{V}}_{\mathrm{o}}$. If the same surface is illuminated with radiation of wavelength $2\lambda$, the stopping potential becomes $\frac{{\mathrm{V}}_{\mathrm{o}}}{4}$. The thre …

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B . If and B are decay constants of A and B respectively, then choose the correct relation from the given options.

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $\mathrm{x}\times 10^{15})\mathrm{Hz}$. The value of …

A proton and an $\alpha$-particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of their de-Broglie wavelength is:

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

A common example of alpha decay is
${}_{92}^{238}\mathrm{U}⟶{}_{90}^{234}\mathrm{Th}+{}_2{\mathrm{He}}^4+\mathrm{Q}$
Given :
${}_{92}^{238}\mathrm{U}=238.05060\mathrm{u}$,
${}_{90}^{234}\mathrm{Th}=234.04360\mathrm{u}$, …

The difference between threshold wavelengths for two metal surfaces A and B having work function ${\varphi }_{\mathrm{A}}=9\mathrm{eV}$ and ${\varphi }_{\mathrm{B}}=4.5\mathrm{eV}$ in nm is:
(Given, hc $=1242\mathrm{eV}\mathrm{nm}$ )

${}_{92}^{238}A{\to }_{90}^{234}B{+}_2^{4}D+Q$

In the given nuclear reaction, the approximate amount of energy released will be :
[Given, mass of ${}_{92}^{238}A=238.05079\times 931.5$ MeV/c${}^2$,
mass of ${}_{90}^{234}B=234.04363\times 931.5$ MeV/c${}^2$
mass of …

The radius of $2^{\text{nd}}$ orbit of ${\text{He}}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of ${\text{Be}}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x:1$. The value of $x$ is ______.

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 practically independent of the atomic number for nuclei of mass number in the range 30 to 170.
Reason R : Nuclear force is short r …

Given below are two statements:

Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.

Statement II : Above the threshold frequency, the maximum kinetic energy of photoe …

An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm . The net energy absorbed by the atom in this process is $\mathrm{n}\times 10^{-4}\mathrm{eV}$. The value of n is ______.
[Assume the atom to be stationary during the absorption and emis …

The half-life of a radioactive nucleus is 5 years, The fraction of the original sample that would decay in 15 years is :

The de Broglie wavelength of an electron having kinetic energy E is $\lambda$. If the kinetic energy of electron becomes $\frac{E}{4}$, then its de-Broglie wavelength will be :

As per given figure A, B and C are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths (i.e. $\frac{{\lambda }_1}{{\lambda }_2}$) is $\frac{7}{4n}$, then the value of $n$ will be

The kinetic energy of an electron, $\alpha$-particle and a proton are given as $4K$, $2K$ and K respectively. The de-Broglie wavelength associated with electron ($\lambda e$) $\alpha$-particle ($\lambda \alpha$) and the proton ($\lambda p$) are as follows:

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

The radius of fifth orbit of the ${\mathrm{Li}}^{++}$ is $\_\_\_\_$ $\times 10^{-12}$ m. Take : radius of hydrogen atom $=0.51\mathring{A}$

The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy:
(Assume ${\mathrm{m}}_{\mathrm{p}}={\mathrm{m}}_{\mathrm{e}}\times 1849$)

The energy of ${\mathrm{He}}^{+}$ ion in its first excited state is. (The ground state energy for the Hydrogen atom is -13.6 eV ):

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

The mass of proton, neutron and helium nucleus are respectively $1.0073\mathrm{u},1.0087\mathrm{u}$ and 4.0015u.
The binding energy of helium nucleus is:

A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi }\times 10^{-17}\mathrm{eVs}$. The value of $x$ is \ …

From the photoelectric effect experiment, following observations are made. Identify which of these are correct
A. The stopping potential depends only on the work function of the metal.
B. The saturation current increases as the intensity of incident light increases.
C. The maximu …

Consider the following radioactive decay process
${}_{84}^{218}A\stackrel{\alpha }{\to }{A}_1\stackrel{\beta }{\to }{A}_2\stackrel{\gamma }{\to }{A}_3\stackrel{\alpha }{\to }{A}_4\stackrel{{\beta }^{+}}{\to }{A}_5\stackrel{\gamma }{\to }{A}_6$
The mass number and the atomic number …

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times 10^{-27}$ kg and radius of nucleus is $1.5\times 10^{-15}{A}^{1/3}$ m. The approximate ratio of the nuclear density and water density is $n\times 10^{13}$. The value of n is ______.

An $\alpha$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

A photon is emitted in transition from $n=4$ to $n=1$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $\mathrm{h}=4\times 10^{-15}\mathrm{eVs}$) :

The energy released per fission of nucleus of ${}^{240}\mathrm{X}$ is 200 MeV. The energy released if all the atoms in 120 g of pure ${}^{240}\mathrm{X}$ undergo fission is ____ $\times 10^{25}$ MeV.
(Given ${\mathrm{N}}_{\mathrm{A}}=6\times 10^{23}$)

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of ${\lambda }_{\mathrm{o}}$. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be:

The ratio of the density of oxygen nucleus ${(}_8^{16}\mathrm{O})$ and helium nucleus ${(}_2^4\mathrm{He})$ is

The wavelength of the radiation emitted is ${\lambda }_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation …

The energy levels of an atom is shown is figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? Given ( $\mathrm{h}=6.62\times 10^{-34}\mathrm{Js}$ )

Given below are two statements :

Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source.

Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.

In the …

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3:2$. The ratio of their nuclear sizes will be ${\left(\frac{x}{3}\right)}^{\frac{1}{3}}$. The value of 'x' is:

The threshold wavelength for photoelectric emission from a material is $5500\mathring{A}$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. 75 W infra-red lamp
B. 10 W infra-red lamp
C. 75 W ultra-violet lamp
D. 10 W ultra-violet …

If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be :

A radioactive element ${}_{92}^{242}\mathrm{X}$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${}_{\mathrm{P}}^{234}\mathrm{Y}$. The value of P is

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A a …

The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{\mathrm{m}}}$, the value of m is

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The nuclear density of nuclides ${}_5^{10}\mathrm{B},{}_3^6\mathrm{Li},{}_{26}^{56}\mathrm{Fe},{}_{10}^{20}\mathrm{Ne}$ and …

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to ${\mathrm{V}}_2$, its de-Broglie wavelength increases by $50\%$. The value of $\left(\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}\right)$ is equal …

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be $\frac{\alpha }{11}$ s. The value of $\alpha$ is ______.