JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

An \( \alpha \) particle and a carbon \( 12 \) atom has same kinetic energy \( K \). The ratio of their de-Broglie wavelengths \( \left( \lambda_{\alpha} : \lambda_{C_{12}} \right) \) is:

\( \dfrac{x}{x+4} \) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) Third permitted energy level to the second level and
(ii) The highest permitted energy level to the second permitted level.
The value of \( x \) will be _______.

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

With reference to the observations in photo-electric effect, identify the correct statements from below:
(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.
(B) The value of saturation current increases on moving the source of light away from the metal surface.
(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light.
(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.
(E) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves.
Choose the correct answer from the options given below:

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

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

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:

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, \( K_p \) are related as:

A proton, a neutron, an electron and an \( \alpha \) – particle have same energy. If \( \lambda_p, \lambda_n, \lambda_e \) and \( \lambda_{\alpha} \) are the de Broglie’s wavelengths of proton, neutron, electron and \( \alpha \) particle respectively, then choose the correct relation from the following:

Find the ratio of energies of photons produced due to transition of an electron 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.

The magnetic moment of an electron (\( e \)) revolving in an orbit around nucleus with an orbital angular momentum is given by :

The equation \( \lambda = \dfrac{1.227}{x} \, \text{nm} \) can be used to find the de-Brogli wavelength of an electron. In this equation \( x \) stands for
Where \( m = \) mass of electron
\( P = \) momentum of electron
\( K = \) Kinetic energy of electron
\( V = \) Accelerating potential in volts for electron

Choose the correct option from the following options given below:

An electron with speed \( v \) and a photon with speed \( c \) have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are \( E_{e} \) and \( p_{e} \) and that of photon are \( E_{ph} \) and \( p_{ph} \) respectively. Which of the following is correct?

In the following nuclear reaction,

Mass number of \( D \) is \( 182 \) and atomic number is \( 74 \). Mass number and atomic number of \( D_{4} \) respectively will be:

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.

What is the half-life period of a radioactive material if its activity drops to \( {1}/{16}^{th} \) of its initial value in \( 30 \) years?

Which of the following figure represents the variation of \( l_n\!\left(\dfrac{R}{R_{0}}\right) \) with \( l_n A \) (if \( R = \) radius of a nucleus and \( A = \) its mass number)

A radioactive nucleus can decay by two different processes. Half-life for the first process is \( 3.0 \) hours while it is \( 4.5 \) hours for the second process. The effective half-life of the nucleus will be:

Mass numbers of two nuclei are in the ratio of \( 4:3 \). Their nuclear densities will be in the ratio of:

The activity of a radioactive material is \( 6.4 \times 10^{-4} \, \text{curie} \). Its half life is \( 5 \, \text{days} \). The activity will become \( 5 \times 10^{-6} \, \text{curie} \) after:

The momentum of an electron revolving in \( n^{\text{th}} \) orbit is given by: (Symbols have their usual meanings)

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 \( v_{2} \). If \( v_{2} = x \, v_{1} \), the value of \( x \) will be ______________.

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

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength  6630 Å  is \( 0.42 \, \text{V} \). If the threshold frequency is \( x \times 10^{13} \,/ \text{s}^{} \), where \( x \) is _______ (nearest integer).
(Given, speed light \( 3 \times 10^{8} \, \text{m} \, /\text{s}^{} \), Planck’s constant \( = 6.63 \times 10^{-34} \, \text{J} \, \text{s} \))

Let \( K_{1} \) and \( K_{2} \) be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength \( \lambda_{1} \) and \( \lambda_{2} \), respectively are incident on a metallic surface. If \( \lambda_{1} = 3 \lambda_{2} \) then:

The ratio of wavelengths of proton and deuteron accelerated by potential \( V_p \) and \( V_d \) is \( 1:\sqrt{2} \). Then, the ratio of \( V_p \) to \( V_d \) will be:

A metal exposed to light of wavelength \( 800\,\text{nm} \) and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength \( 500\,\text{nm} \) is used. The workfunction of the metal is: (Take \( hc=1230\,\text{eV}\!\cdot\!\text{nm} \)).

The electric field at a point associated with a light wave is given by \( E = 200 \left[\sin(6 \times 10^{15} )t + \sin(9 \times 10^{15} )t\right] \, \text{V m}^{-1} \)
Given: \( h = 4.14 \times 10^{-15} \, \text{eV s} \)
If this light falls on a metal surface having a work function of \( 2.50 \, \text{eV} \), the maximum kinetic energy of the photoelectrons will be:

Given below are two statements:
Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \( (E_1) \) to higher energy orbit \( (E_2) \), is given as \( h f = E_1 - E_2 \)
Statement II: The jumping of electron from higher energy orbit \( (E_2) \) to lower energy orbit \( (E_1) \) is associated with frequency of radiation given as \( f = (E_2 - E_1)/h \). This condition is Bohr’s frequency condition.
In the light of the above statements, choose the correct answer from the options given below:

A nucleus of mass \( M \) at rest splits into two parts having masses \( \dfrac{M'}{3} \) and \( \dfrac{2M'}{3} \) \( (M' < M) \). The ratio of de Broglie wavelength of two parts will be:

A metal surface is illuminated by a radiation of wavelength 4500 Å  The ejected photo-electron enters a constant magnetic field of \( 2 \, \text{mT} \) making an angle of \( 90^{\circ} \) with the magnetic field. If it starts revolving in a circular path of radius \( 2 \, \text{mm} \), the work function of the metal is approximately:

The half-life of a radioactive substance is \( 5 \, \text{years} \). After \( x \) years a given sample of the radioactive substance gets reduced to \( 6.25\% \) of its initial value. The value of \( x \) is ______.

A radioactive sample decays \( \dfrac{7}{8} \) times its original quantity in \( 15 \, \text{min} \). The half-life of the sample is:

Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be:

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
\( \, ^{2}_{1}X + \, ^{2}_{1}X = \, ^{4}_{2}Y \)
The binding energies per nucleon for \( \, ^{2}_{1}X \) and \( \, ^{4}_{2}Y \) are \( 1.1 \, \text{MeV} \) and \( 7.6 \, \text{MeV} \) respectively. The energy released in this process is ________ \( \text{MeV} \).

Following statements related to radioactivity are given below:
(\( a \)) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(\( b \)) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(\( c \)) Slope of the graph of \( \log_{e} \) (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time \( ( \tau ) \).
(\( d \)) Product of decay constant \( ( \lambda ) \) and half-life time \( ( T_{1/2} ) \) is not constant.
Choose the most appropriate answer from the options given below:

The half life period of a radioactive substance is \( 60 \, \text{days} \). The time taken for \( \dfrac{7}{8} \) th of its original mass to disintegrate will be:

\( \sqrt{d_1} \) and \( \sqrt{d_2} \) are the impact parameters corresponding to scattering angles \( 60^\circ \) and \( 90^\circ \) respectively, when an \( \alpha \) particle is approaching a gold nucleus. For \( d_1 = x d_2 \), the value of \( x \) will be __________.

In the hydrogen spectrum, \( \lambda \) be the wavelength of first transition line of Lyman series. The wavelength difference will be “\( a\lambda \)” between the wavelength of \( 3^\text{rd} \) transition line of Paschen series and that of \( 2^\text{nd} \) transition line of Balmer series where \( a = \) _______.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal.
Reason R : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.
In the light of the above statements, choose the most appropriate answer from the options given below.

A sample contains \( 10^{-2} \) \( \text{kg} \) each of two substances \( A \) and \( B \) with half lives \( 4 \, \text{s} \) and \( 8 \, \text{s} \) respectively. The ratio of their atomic weights is \( 1:2 \). The ratio of the amounts of \( A \) and \( B \) after \( 16 \, \text{s} \) is \( \dfrac{x}{100} \). The value of \( x \) is ________.

Given below are two statements :

In the light of the above statements choose the correct answer from the option given below :

The de Broglie wavelengths for an electron and a photon are \( \lambda_e \) and \( \lambda_p \) respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?