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The ratio of the power of a light source \( S_1 \) to that the light source \( S_2 \) is \( 2 \). \( S_1 \) is emitting \( 2 \times 10^{15} \) photons per second at \( 600 \, \text{nm} \). If the wavelength of the source \( S_2 \) is \( 300 \, \text{nm} \), then the number of photons per second emitted by \( S_2 \) is __________ \( \times 10^{14} \).

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

The work function of a metal is \( 3 \ \text{eV} \). The color of the visible light that is required to cause emission of photoelectrons is:

An electron projected perpendicular to a uniform magnetic field \( B \) moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is:

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is:

Given below are two statements:
Statement (I): The dimensions of Planck's constant and angular momentum are same.
Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.
In the light of the above statements, choose the most appropriate answer from the options given below:

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \( \text{Li}^{++} \) ion in its ground state is given by \( \frac{1}{X} a_{0} \), where \( X = \) _____________.
(Where \( a_{0} \) is the first Bohr's radius.)

A light source of wavelength \( \lambda \) illuminates a metal surface and electrons are ejected with maximum kinetic energy of \( 2\,\text{eV} \). 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: (The work function of metal is \( 1\,\text{eV} \))

Match the List-I with List-II:

Choose the correct answer from the options given below:

A photoemissive substance is illuminated with a radiation of wavelength \( \lambda_i \) so that it releases electrons with de-Broglie wavelength \( \lambda_e \). The longest wavelength of radiation that can emit photoelectron is \( \lambda_0 \). Expression for de-Broglie wavelength is given by:
(\( m \) : mass of the electron, \( h \) : Planck’s constant and \( c \) : speed of light)

The energy \( E \) and momentum \( p \) of a moving body of mass \( m \) are related by some equation. Given that \( c \) represents the speed of light, identify the correct equation

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): Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below:

In a hydrogen like ion, the energy difference between the \( 2^{\text{nd}} \) excitation energy state and ground is \( 108.8 \, \text{eV} \). The atomic number of the ion 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 (R): A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.
In the light of the above statements, choose the most appropriate answer from the options given below:

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '- \( \sigma \)'. The rate of change of de-Broglie wave length associated with the electron varies inversely as \( n^{\text{th}} \) power of time. The numerical value of \( n \) is _______.

A small mirror of mass \( m \) is suspended by a massless thread of length \( l \), then the small angle through which the thread will be deflected when a short pulse of laser of energy \( E \) falls normal on the mirror: \( ( c = \) speed of light in vacuum and \( g = \) acceleration due to gravity \( ) \)

An electron in the hydrogen atom initially in the fourth excited state makes a transition to \( n^{\text{th}} \) energy state by emitting a photon of energy \( 2.86 \, \text{eV} \). The integer value of \( n \) will be __________.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(( {}^{64}_{29}\text{Cu} )\) nucleus is greater than that of the carbon \(( {}^{12}_{6}\text{C}) \) nucleus.
Reason (R) : The nucleus of mass number \( A \) has radius proportional to \( A^{1/3} \). In the light of the above statements, choose the most appropriate answer from the options given below :

A radioactive nucleus \( n_{2} \) has \( 3 \) times the decay constant as compared to the decay constant of another radioactive nucleus \( n_{1} \). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \( n_{2} \) to the number of nuclei of \( n_{1} \), after one half-life of \( n_{1} \)?

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

Choose the correct nuclear process from the below options:

[$p$ : proton, $n$ : neutron, $e^-$ : electron, $e^+$ : positron, $\nu$ : neutrino, $\bar{\nu}$ : antineutrino]

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is \( 2000 \, Å \) and it becomes \( 6000 \, Å \) when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is:

A proton of mass '$m_p$' has same energy as that of a photon of wavelength '$\lambda$'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is:

The work functions of cesium (Cs) and lithium (Li) metals are \( 1.9 \, \text{eV} \) and \( 2.5 \, \text{eV} \), respectively. If we incident a light of wavelength \( 550 \, \text{nm} \) on these two metal surfaces, then photo-electric effect is possible for the case of:

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:

In an experiment with photoelectric effect, the stopping potential.

Considering Bohr's atomic model for hydrogen atom:
(A) the energy of H atom in ground state is same as energy of \( \mathrm{He^{+}} \) ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \( \mathrm{Li^{++}} \) ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \( \mathrm{He^{+}} \) ion for its ground state.
(D) the energy of \( \mathrm{He^{+}} \) ion in its first excited state is same as that for \( \mathrm{Li^{++}} \) ion in its ground state.
Choose the correct answer from the options given below:

In photoelectric effect, the stopping potential \( (V_{0}) \) v/s frequency \( (\nu) \) curve is plotted. (\( h \) is the Planck’s constant and \( \phi_{0} \) is work function of metal)
(A) \( V_{0} \,\text{v/s}\, \nu \) is linear
(B) The slope of \( V_{0} \,\text{v/s}\, \nu \) curve \( = \dfrac{\phi_{0}}{h} \)
(C) \( h \) constant is related to the slope of \( V_{0} \,\text{v/s}\, \nu \) line
(D) The value of electric charge of electron is not required to determine \( h \) using the \( V_{0} \,\text{v/s}\, \nu \) curve
(E) The work function can be estimated without knowing the value of \( h \).
Choose the correct answer from the options given below:

Energy released when two deuterons \( ({}_{1}H^{2})\) fuse to form a helium nucleus \( ({}_{2}He^{4}) \) is:
(Given: Binding energy per nucleon of \( {}_{1}H^{2} = 1.1 \, \text{MeV} \) and binding energy per nucleon of \( {}_{2}He^{4} = 7.0 \, \text{MeV} \))

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

For a nucleus of mass number \( A \) and radius \( R \), the mass density of nucleus can be represented as:

The frequency of revolution of the electron in Bohr’s orbit varies with \( n \), the principal quantum number as:

A monochromatic light is incident on a metallic plate having work function \( \phi \). An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is: \( \) (Given: The magnitude of charge of an electron is \( e \) and mass is \( m \), \( h \) is Planck's constant and \( c \) is velocity of light. Take the magnetic field exists throughout the path of electron)

An electron with mass ‘\( m \)’ with an initial velocity \( (t = 0) \, \vec{v} = -v_{0}\,\hat{i} \; (v_{0} > 0) \) enters a magnetic field \( \vec{B} = B_{0}\,\hat{j} \). If the initial de-Broglie wavelength at \( t = 0 \) is \( \lambda_{0} \) then its value after time ‘\( t \)’ would be:

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of \( 5^{\text{th}} \) orbit of the electron in \( \mathrm{Li}^{2+} \) and \( \mathrm{He}^{+} \) is:

An electron of mass \( 'm' \) with an initial velocity \( \vec{v} = v_{0}\,\hat{i} \) (\( v_{0} > 0 \)) enters an electric field \( \vec{E} = -E_{0}\,\hat{k} \). If the initial de Broglie wavelength is \( \lambda_{0} \), the value after time \( t \) would be:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
Reason R: The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements, choose the correct answer from the options given below:

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JEE Main 2025 3rd April Evening Shift

An electron in the hydrogen atom initially in the fourth excited state makes a transition to \( n^{\text{th}} \) energy state by emitting a photon of energy \( 2.86 \, \text{eV} \). The integer value of \( n \) will be __________.