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Light is incident on a metallic plate having work function \(110 \times 10^{-20} \, \text{J}\). If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ________ \( \text{rad/s} \). \( (h = 6.63 \times 10^{-34} \, \text{J s} )\).

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is \( 3.2 \, \text{V} \). If a second light having wavelength twice of first light is used, the stopping potential drops to \( 0.7 \, \text{V} \). The wavelength of first light is __________ m.
\( (h = 6.63 \times 10^{-34} \, \text{J}\cdot\text{s}, \; e = 1.6 \times 10^{-19} \, \text{C}, \; c = 3 \times 10^{8} \, \text{m/s}) \)

The de Broglie wavelength for an electron accelerated through the potential difference of \( V_1 \) volt is \( \lambda_1 \). When the potential difference is changed to \( V_2 \) volt, the associated de Broglie wavelength is increased by \( 50\% \). If \( (V_1/V_2) = (9/\alpha) \), then the value of \( \alpha \) is ________.

The de Broglie wavelength associated with an electron accelerated through a potential difference \( V \) is \( \lambda_e \), and the de Broglie wavelength associated with a proton accelerated through the same potential difference is \( \lambda_p \). If their corresponding masses are \( m_e \) and \( m_p \), respectively, then the ratio of their de-Broglie wavelengths \( \left( \frac{\lambda_e}{\lambda_p} \right) \) is _____.

The ratio of momentum of the photons of the \( 1^{\text{st}} \) and \( 2^{\text{nd}} \) line of Balmer series of Hydrogen atoms is \( \alpha / \beta \). The possible values of \( \alpha \) and \( \beta \) are:

The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ______________.

(Assume mass of proton = mass of neutron) :

A monochromatic source of light operating at \( 15 \ \text{kW} \) emits \( 2.5 \times 10^{22} \) photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ______.
[Take \( h = 6.6 \times 10^{-34} \ \text{J}\!\cdot\!\text{s} \) and \( c = 3 \times 10^{8} \ \text{m/s} \)]

For a certain metal, when monochromatic light of wavelength \( \lambda \) is incident, the stopping potential for photoelectrons is \( 3V_{0} \). When the same metal is illuminated by light of wavelength \( 2\lambda \), then the stopping potential becomes \( V_{0} \). The threshold wavelength for photoelectric emission for the given metal is \( \alpha \lambda \). The value of \( \alpha \) is________.

The de-Broglie wavelength of an oxygen molecule at \( 27^\circ \text{C} \) is \( x \times 10^{-12} \, \text{m} \). The value of \( x \) is: [Take Planck’s constant \( = 6.63 \times 10^{-34} \, \text{J}\cdot\text{s} \), Boltzmann constant \( = 1.38 \times 10^{-23} \, \text{J K}^{-1} \), mass of oxygen molecule \( = 5.31 \times 10^{-26} \, \text{kg} \)]

The average energy released per fission for the nucleus of \( {}^{235}_{92}\text{U} \) is \( 190 \, \text{MeV} \). When all the atoms of \( 47 \, \text{g} \) pure \( {}^{235}_{92}\text{U} \) undergo fission process, the energy released is \( a \times 10^{23} \, \text{MeV} \). The value of \( a \) is ______.
(Avogadro Number \( = 6 \times 10^{23} \) per mole)

An electron is travelling with a velocity \( v \) in free space and when it enters a medium, its velocity is reduced by \( 20\% \). The de Broglie wavelength of electron in the medium is \( \alpha \lambda_0 \), where \( \lambda_0 \) is its de Broglie wavelength in free space. The value of \( \alpha \) is ________________ .

An electron of mass \( m \) is moving in an electric field \( \vec{E} = -2E_0 \, \hat{j} \) \( (E_0 = \text{constant} > 0) \), with an initial velocity \( \vec{V} = v_0 \, \hat{i} \) \( (v_0 = \text{constant} > 0) \). If \( \lambda_0 = \dfrac{h}{4 m v_0} \), its de Broglie wavelength at time \( t \) is ______; \( (e = \text{charge of electron}) \).

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2^nd and \( 4 \)th orbits of hydrogen atom __________.

A particle having electric charge \( 3 \times 10^{-19} \; \text{C} \) and mass \( 6 \times 10^{-27} \; \text{kg} \) is accelerated by applying an electric potential of \( 1.21 \; \text{V} \). Wavelength of the matter wave associated with the particle is \( \alpha \times 10^{-12} \; \text{m} \). The value of \( \alpha \) is __________. (Take Planck’s constant \( = 6.6 \times 10^{-34} \; \text{J, s} \))

An atom \( {}^{8}_{3}X \) is bombarded by shower of fundamental particles and in \( 10 \, \text{s} \) this atom absorbed \( 10 \) electrons, \( 10 \) protons and \( 9 \) neutrons. The percentage growth in the surface area of the nucleons is recorded by:

Two nuclei of mass number \( 3 \) combine with another nucleus of mass number \( 4 \) to yield a nucleus of mass number \( 10 \). If the binding energy per nucleon for the mass numbers \( 3 \), \( 4 \) and \( 10 \) are \( 5.6 \, \text{MeV} \), \( 7.4 \, \text{MeV} \) and \( 6.1 \, \text{MeV} \), respectively, then in the process,

The binding energy per nucleon of \( ^{209}_{83}\mathrm{Bi} \) is ________ \( \text{MeV} \).
[Take \( m\!\left(^{209}_{83}\mathrm{Bi}\right) = 208.980388\,\text{u} \), \( m_p = 1.007825\,\text{u} \), \( m_n = 1.008665\,\text{u} \), \( 1\,\text{u} = 931\,\text{MeV}/c^{2} \)]

Which of the following pair of nuclei are isobars of the element?

The minimum frequency of photon required to break a particle of mass \( 15.348 \) amu into \( 4 \alpha \) particles is __________ kHz.
[ mass of He nucleus \(=4.002\) amu, \(1\) amu \(=1.66\times 10^{-27}\) kg, \( h=6.6\times 10^{-34} \) J.s and \( c=3\times 10^{8} \) m/s ]

The graph shows variation of stopping potential \( V_0 \) with the frequency \( \nu \) of the incident radiation for three photosensitive metals \( X_1 \), \( X_2 \), and \( X_3 \). Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

A light wave described by \( E = 60 \left[ \sin\!\left(3 \times 10^{15} \right) t+ \sin\!\left(12 \times 10^{15} \right)t \right] \) (in SI units) falls on a metal surface of work function \( 2.8 \, \text{eV} \). The maximum kinetic energy of ejected photoelectron is (approximately) ____________ \( \text{eV} \).
\( ( h = 6.6 \times 10^{-34} \, \text{J}\!\cdot\!\text{s}, \text{ and } e = 1.6 \times 10^{-19} \, \text{C} ) \)

The binding energy for the following nuclear reactions are expressed in \( \text{MeV} \).
\( {}_{2}\mathrm{He}^{3} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{4} + 20 \, \text{MeV} \)
\( {}_{2}\mathrm{He}^{4} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{5} - 0.9 \, \text{MeV} \)
If \( x_{3}, x_{4}, x_{5} \) denote the stability of \( {}_{2}\mathrm{He}^{3}, {}_{2}\mathrm{He}^{4} \) and \( {}_{2}\mathrm{He}^{5} \), respectively, then the correct order is:

Given below are two statements:

Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.

Statement II: For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.

In the light of the above statements, choose the correct answer from the options given below.

Assuming the experimental mass of \( ^{12}_{6}\mathrm{C} \) as \( 12\,u \), the mass defect of \( ^{12}_{6}\mathrm{C} \) atom is ____________ \( \text{MeV}/c^2 \).
(Mass of proton \( = 1.00727\,u \). mass of neutron \( = 1.0866\,u \), \( 1\,u = 931.5\, \text{MeV}/c^2 \) and \( c \) is the speed of the light in vacuum).

Light source having wavelength \( 331 \, \text{nm} \) is used to generate photo-electrons whose stopping potential is \( 0.2 \, \text{V} \). The work function of the used metal in the experiment is \( \alpha \times 10^{-19} \, \text{J} \). The value of \( \alpha \) is ______.
\( (h = 6.62 \times 10^{-34} \, \text{J s} , \, e = 1.6 \times 10^{-19} \, \text{C} \text{ and } c = 3 \times 10^{8} \, \text{m/s}) \)

In the hydrogen atom, the electron makes a transition from the higher orbit \( (i) \) to a lower orbit \( (f) \). The ratio of the radius of the orbits in given by \( r_i : r_f = 16 : 4 \). The wavelength of photon emitted due to this transition is _____ \( \text{nm} \).
\( \text{(Given Rydberg constant} = 1.0973 \times 10^{7} / \text{m)} \)

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

Two electrons are moving in orbits of two hydrogen like atoms with speeds \( 3 \times 10^5 \, \text{m/s} \) and \( 2.5 \times 10^5 \, \text{m/s} \) respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.

Angular momentum of an electron in a hydrogen atom is \( \dfrac{3h}{\pi} \), then the energy of the electron is ______ \( \text{eV} \).

\( K_1 \) and \( K_2 \) be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength \( \lambda_1 \) and \( \lambda_2 \), respectively. If \( \lambda_1 = 2\lambda_2 \) then the work function of material is given by:

If an alpha particle with energy \( 7.7 \, \text{MeV} \) is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ____________ \( \text{m} \). \( \text{(Atomic number of gold } = 79 \text{ and } \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^{9} \text{ in SI units)} \)

Two radioactive substances \( A \) and \( B \) of mass numbers \( 200 \) and \( 212 \) respectively, shows spontaneous \( \alpha \)-decay with same \( Q \) value of \( 1 \, \text{MeV} \). The ratio of energies of \( \alpha \)-rays produced by \( A \) and \( B \) is ______.

In hydrogen atom spectrum, (\( R \rightarrow \) Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is \( \dfrac{4}{3R} \)
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is \( \dfrac{9}{R} \)
D. the minimum wavelength of Lyman series is \( \dfrac{5}{4R} \)
Choose the correct answer from the options given below:

The energy released when \( \frac{7}{17.13} \) \( \text{kg} \) of \( {}^{7}_{3}\mathrm{Li} \) is converted into \( {}^{4}_{2}\mathrm{He} \) by proton bombardment is \( \alpha \times 10^{32} \) \( \text{eV} \). The value of \( \alpha \) is _______. (Nearest integer) (Mass of \( {}^{7}_{3}\mathrm{Li} = 7.0183\,u \), mass of \( {}^{4}_{2}\mathrm{He} = 4.0004\,u \), mass of proton \( = 1.008\,u \) and \( 1u = 931\,\mathrm{MeV}/c^{2} \) and Avogadro number \( = 6.0 \times 10^{23} \))

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JEE MAIN 2026 28TH Jan Morning Shift

The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ______________.

(Assume mass of proton = mass of neutron) :