Modern Physics — JEE Main PYQs

How many alpha and beta particles are emitted when Uranium ${}_{92}{\mathrm{U}}^{238}$ decays to lead ${}_{82}{\mathrm{Pb}}^{206}$ ?

An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength $\left({\lambda }_a:{\lambda }_{C12}\right)$ is :

A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (Given, Plank's constant $=6.6\times 10^{-34}\mathrm{Js}$)

A beam of monochromatic light is used to excite the electron in ${\mathrm{Li}}^{++}$from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x\times 10^{-10}m$. The value of x is ____ .
[Given hc $=1242\mathrm{eV}\mathrm{nm}$ ]

The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength :

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its(i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Choose the correct option from the following options given below :
(A) In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
(B) An atom has a nearly continuous mass distribution in a Ruthe …

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is $v_1$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes $v_2$ …

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectivly will be :

In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

A sample contains $10^{-2}\mathrm{kg}$ each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of then atomic weights is $1:2$. The ratio of the amounts of $A$ and $B$ after $16s$ is $\frac{x}{100}$. the value of $x$ is $\_\_\_\_$.

A proton, a neutron, an electron and an $\alpha$-particle have same energy. If ${\lambda }_{\mathrm{p}},{\lambda }_{\mathrm{n}},{\lambda }_{\mathrm{e}}$ and ${\lambda }_{\alpha }$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose t …

Which of the following figure represents the variation of $\ln \left(\frac{\mathrm{R}}{{\mathrm{R}}_0}\right)$ with $\ln \mathrm{A}$ (If $\mathrm{R}=$ radius of a nucleus and $\mathrm{A}=$ its mass number)

Given below are two statements:
Statement I: Davisson-Germer experiment establishes the wave nature of electrons.
Statement II: If electrons have wave nature, they can interfere and show diffraction.
In the light of the above statements choose the correct answer from the options …

The ratio for the speed of the electron in the $3^{\text{rd}}$ orbit of ${\mathrm{He}}^{+}$ to the speed of the electron in the $3^{\text{rd}}$ orbit of hydrogen atom will be:

In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $\varphi =2.5\mathrm{eV}$. If the wavelength of incident light is switched to 400 nm , find out the change in the stopping potential. …

A particular hydrogen like ion emits radiation of frequency $2.92\times 10^{15}\mathrm{Hz}$ when it makes transition from $n=3$ to $n=1$. The frequency in Hz of radiation emitted in transition from $n=2$ to $n=1$ will be :

Given below are two statements:
Statements I: Two photons having equal linear momenta have equal wavelengths
Statements II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the corr …

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$, $\mathrm{D}$ and E. The transitions $\mathrm{A}$, $\mathrm{B}$ and C respectively represent:

The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to $75\%$ of the initial value?

At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_A(0)=2N_B(0)$. The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to B and B disintegrates to $C$. Which of the following figures represe …

A nucleus of mass M emits $\gamma$-ray photon of frequency 'v'. The loss of internal energy by the nucleus is: [Take 'c' as the speed of electromagnetic wave]

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take $\ln 3=1.1$)

The radiation corresponding to $3\to 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5\times 10^{-4}\mathrm{T}$. Assume that the radius of the largest circular circular path f …

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

An X - ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

The de Broglie wavelength of a proton and $\alpha$- particle are equal. The ratio of their velocities is:

An electron having de-Broglie wavelength $\lambda$ is indent on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:

For a certain radioactive process the graph between $\ln (R)$ and $t(\text{sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :

A radioactive substance decays to ${\left(\frac{1}{16}\right)}^{\text{th }}$ of this initial activity in 80 days. The half life of the radioactive substance expressed in days is ____.

A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is $3{\mathrm{V}}_0$. If the same surface is illuminated with a radiation of wavelength $2\lambda$, the stopp …

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm ?

$X$ different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number $\mathrm{n}=6$ ? The value of $X$ is ____.

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200 V . After this, their de Broglie wavelengths are ${\lambda }_{\alpha }$ and ${\lambda }_{\mathrm{P}}$ respectively. The ratio $\frac{{\lambda }_{\mathrm{P}}}{{\lambda }_{\alpha }}$ is :

Two radioactive substances $X$ and $Y$ originally have $N_1$ and $N_2$ nuclei respectively. Half life of $X$ is half of the life of Y . After three half lives of Y , number of nuclei of both are equal.
The ratio $\frac{{\mathrm{N}}_1}{{\mathrm{N}}_2}$ will be equ …

An electron of mass $m_e$ and a proton of mass $m_p$ are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is :

A nucleus with number 184 initially at rest emits an $\alpha$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the $\alpha$-particle.

Consider a situation in which reverse biased current of a particular $\mathrm{P}-\mathrm{N}$ junction increase when it is exposed to a light of wavelength $\le 621\mathrm{nm}$. During this process, enhancement in carrier concentration takes place due to generation of hole - el …

LED is constructed from $\mathrm{Ga}-\mathrm{As}-\mathrm{P}$ semiconducting material. The energy gap of this LED is 1.9 eV . Calculate the wavelength of light emitted and its colour.
$[\mathrm{h}=6.63\times 10^{-34}\mathrm{Js}$ and …

If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of ${\lambda }_1:{\lambda }_2$ is :

Given below are two statements : one is labelled as Assertion A and the other is labeled as Reason R.
Assertion A : An electron microscope achieve better resolving power than an optical microscope.
Reason R : The de Broglie's wavelength of the electrons emitted from an electron g …

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds?
$(\sqrt{2}=1.414)$

In a photoelectric experiment, increasing the intensity of incident light:

A radioactive sample is undergoing $\alpha$ decay. At any time $t_1$, its activity is $A$ and another time $t_2$, the activity is $\frac{\mathrm{A}}{5}$. What is the average life time for the sample?

The recoil speed of a hydrogen atom after it emits a photon in going from $n=5$ state to $n=1$ state will be :

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $\mathrm{x}:\mathrm{y}$. The …

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to:

A free electron of 2.6 eV energy collides with a ${\mathrm{H}}^{+}$ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. ( $\mathrm{h}=6.6\times 10^{-34}\mathrm{Js}$ )

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K .E. and momentum respectively. Then choose the correct option :