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According to Bohr’s theory, the moment of momentum of an electron revolving in \( 4^{\text{th}} \) orbit of hydrogen atom is:

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is:

A star has \( 100\% \) helium composition. It starts to convert three \( ^4\text{He} \) into one \( ^{12}\text{C} \) via triple alpha process as \( ^4\text{He} + ^4\text{He} + ^4\text{He} \rightarrow ^{12}\text{C} + Q \). The mass of the star is \( 2.0 \times 10^{32} \, \text{kg} \) and it generates energy at the rate of \( 5.808 \times 10^{30} \, \text{W} \). The rate of converting these \( ^4\text{He} \) to \( ^{12}\text{C} \) is \( n \times 10^{42} \, \text{s}^{-1} \), where \( n \) is _______.
[Take, mass of \( ^4\text{He} = 4.0026 \, \text{u} \) , mass of \( ^{12}\text{C} = 12 \, \text{u} \) ]

A hydrogen atom changes its state from \( n = 3 \) to \( n = 2 \). Due to recoil, the percentage change in the wavelength of emitted light is approximately \( 1 \times 10^{-n} \). The value of \( n \) is _______________.
[Given \( R h c = 13.6 \, \text{eV} \), \( h c = 1242 \, \text{eV}\,\text{nm} \), \( h = 6.6 \times 10^{-34} \, \text{J}\,\text{s} \), mass of the hydrogen atom \( = 1.6 \times 10^{-27} \, \text{kg} \)]

A hydrogen atom in ground state is given an energy of \( 10.2\,\text{eV} \). How many spectral lines will be emitted due to transition of electrons?

In a hypothetical fission reaction \( {_{92}X^{236}} \rightarrow {_{56}Y^{141}} + {_{36}Z^{92}} + 3R \) The identity of emitted particle \( (R) \) is:

Given below are two statements: one is labelled as Assertion \( (A) \) and the other is labelled as Reason \( (R) \).
Assertion \( (A) \): Number of photons increases with increase in frequency of light.
Reason \( (R) \): Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.
In the light of the above statements, choose the most appropriate answer from the options given below:

A particular hydrogen-like ion emits the radiation of frequency \( 3 \times 10^{15} \, \text{Hz} \) when it makes transition from \( n=2 \) to \( n=1 \). The frequency of radiation emitted in transition from \( n=3 \) to \( n=1 \) is \( \dfrac{x}{9} \times 10^{15} \, \text{Hz} \), when \( x = \) ____________.

The radius of a nucleus of mass number \( 64 \) is \( 4.8 \) fermi. Then the mass number of another nucleus having radius of \( \frac{1000}{x} \) \( 4 \) fermi is ______, where \( x \) is ______.

Hydrogen atom is bombarded with electrons accelerated through a potential difference of \( V \), which causes excitation of hydrogen atoms. If the experiment is being performed at \( T = 0 \, \text{K} \), the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be \( \dfrac{\alpha}{10} \, \text{V} \), where \( \alpha = \) _______.

Given below are two statements:

Statement I: Figure shows the variation of stopping potential the frequency \( (\nu) \) for the two photosensitive materials \( M_1 \) and \( M_2 \). The slope gives value of \( \frac{h}{e} \), where \( h \) is Planck’s constant, \( e \) is the charge of electron.
Statement II: \( M_2 \) will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency.
In the light of the above statements, choose the most appropriate answer from the options given below.

From the statements given below:
(A) The angular momentum of an electron in \( n^{\text{th}} \) orbit is an integral multiple of \( \hbar \).
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear forces are central and charge independent.
(E) Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below:

Given below are two statements:
Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.
Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.
In the light of the above statements, choose the most appropriate from the options given below.

In a photoelectric effect experiment a light of frequency \( 1.5 \) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electron emitted will be:

If a nuclear fission reaction of an isotope of mass \( M \), three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \( \Delta M \) will be:

The atomic mass of \( _{6}\mathrm{C}^{12} \) is \( 12.000000 \, \text{u} \) and that of \( _{6}\mathrm{C}^{13} \) is \( 13.003354 \, \text{u} \). The required energy to remove a neutron from \( _{6}\mathrm{C}^{13} \), if mass of neutron is \( 1.008665 \, \text{u} \), will be:

Which of the following nuclear fragments corresponding to nuclear fission between neutron \(( ^{1}_{0}\mathrm{n}) \) and uranium isotope \(( ^{235}_{92}\mathrm{U} \)) is correct:

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ________ \( \times 10^{-2} \, \text{MeV} \). (Given \( 1 \, u = 931 \, \text{MeV} / c^{2} \), atomic mass of helium = \( 4.002603 \, u \).)

The energy released in the fusion of \( 2 \, \text{kg} \) of hydrogen deep in the sun is \( E_H \) and the energy released in the fission of \( 2 \, \text{kg} \) \( {}^{235}\!U \) is \( E_U \). The ratio \( \dfrac{E_H}{E_U} \) is approximately:
(Consider the fusion reaction as \( 4\,{}^{1}_{1}\!H + 2e^{-} \rightarrow {}^{4}_{2}\!He + 2\nu + 6\gamma + 26.7 \, \text{MeV} \) , energy released in the fission reaction of \( {}^{235}\!U \) is \( 200 \, \text{MeV} \) per fission nucleus and \( N_A = 6.023 \times 10^{23} \))

When UV light of wavelength \( 300 \, \text{nm} \) is incident on the metal surface having work function \( 2.13 \, \text{eV} \), electron emission takes place. The stopping potential is:
(Given \( hc = 1240 \, \text{eV nm} \))

A electron of hydrogen atom on an excited state is having energy \( E_n = -0.85 \, \text{eV} \). The maximum number of allowed transitions to lower energy level is________.

In photoelectric experiment energy of \( 2.48 \, \text{eV} \) irradiates a photo sensitive material. The stopping potential was measured to be \( 0.5 \, \text{V} \). Work function of the photo sensitive material is:

An electron rotates in a circle around a nucleus having positive charge \( Ze \). Correct relation between total energy \( E \) of electron to its potential energy \( U \) is:

In an alpha particle scattering experiment distance of closest approach for the \( \alpha \) particle is \( 4.5 \times 10^{-14} \, \text{m} \). If target nucleus has atomic number \( 80 \), then maximum velocity of \( \alpha \)-particle is ______ \( \times 10^{5} \, \text{m} / \text{s} \) approximately.
[\( \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{9} \) SI unit, mass of \( \alpha \) particle \( = 6.72 \times 10^{-27} \, \text{kg} \)]

The acceptor level of a p-type semiconductor is \( 6 \, \text{eV} \). The maximum wavelength of light which can create a hole would be:
Given \( hc = 1242 \, \text{eV nm} \).

The de-Broglie wavelengths of a proton and an \( \alpha \) particle are \( \lambda \) and \( 2\lambda \) respectively. The ratio of the velocities of proton and \( \alpha \) particle will be:

The work function of a substance is \( 3.0 \, \text{eV} \). The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately.

The disintegration energy \( Q \) for the nuclear fission of \( {}^{235}\!U \rightarrow {}^{140}\!Ce + {}^{94}\!Zr + n \) is ____________ \( \text{MeV} \).
Given atomic masses of \( {}^{235}\!U : 235.0439 \, u \); \( {}^{140}\!Ce : 139.9054 \, u \), \( {}^{94}\!Zr : 93.9063 \, u \); \( n : 1.0086 \, u \),
Value of \( c^{2} = 931 \, \text{MeV} / u \).

An object is placed in a medium of refractive index \( 3 \). An electromagnetic wave of intensity \( 6 \times 10^{8} \ \text{W}/\text{m}^{2} \) falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space \( 3 \times 10^{8} \ \text{m}/\text{s} \) ):

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \( 5^{\text{th}} \) excited state of a hydrogen atom is:

If Rydberg’s constant is \( R \), the longest wavelength of radiation in Paschen series will be \( \dfrac{\alpha}{7R} \), where \( \alpha = \) ________________ .

In a nuclear fission process, a high mass nuclide \( (A \approx 236) \) with binding energy \( 7.6 \, \text{MeV/Nucleon} \) dissociated into middle mass nuclides \( (A \approx 118) \), having binding energy of \( 8.6 \, \text{MeV/Nucleon} \). The energy released in the process would be __________ \( \text{MeV} \).

If the wavelength of the first member of Lyman series of hydrogen is \( \lambda \). The wavelength of the second member will be:

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \( 2:1 \). After disintegration they will move:

UV light of \( 4.13 \, \text{eV} \) is incident on a photosensitive metal surface having work function \( 3.13 \, \text{eV} \). The maximum kinetic energy of ejected photoelectrons will be:

Which of the following statement is not true about stopping potential \( (V_0) \)?

A convex lens of focal length \( 40 \, \text{cm} \) forms an image of an extended source of light on a photo electric cell. A current \( I \) is produced. The lens is replaced by another convex lens having the same diameter but focal length \( 20 \, \text{cm} \). The photoelectric current now is :

If \( M_0 \) is the mass of isotope \( ^{12}_{5}B \), \( M_p \) and \( M_n \) are the masses of proton and neutron, the nuclear binding energy of isotope is:

In Frank-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at \( 10.2 \, \text{V} \). The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _______ \( \text{nm} \).
(Given \( hc = 1245 \, \text{eV nm}, \, e = 1.6 \times 10^{-19} \, C \))

For the photoelectric effect, the maximum kinetic energy \( (E_k) \) of the photoelectrons is plotted against the frequency \( (v) \) of the incident photons as shown in figure. The slope of the graph gives

The explosive in a Hydrogen bomb is a mixture of ${}_1\text{H}^2$, ${}_1\text{H}^3$ and ${}_3\text{Li}^6$ in some condensed form. The chain reaction is given by:

${}_3\text{Li}^6 + {}_0\text{n}^1 \rightarrow {}_2\text{He}^4 + {}_1\text{H}^3$

${}_1\text{H}^2 + {}_1\text{H}^3 \rightarrow {}_2\text{He}^4 + {}_0\text{n}^1$

During the explosion the energy released is approximately:

[Given: $M(\text{Li}) = 6.01690\text{ amu}$, $M({}_1\text{H}^2) = 2.01471\text{ amu}$, $M({}_2\text{He}^4) = 4.00388\text{ amu}$ and $1\text{ amu} = 931.5\text{ MeV}$]

An electron revolving in \( n^{\text{th}} \) Bohr orbit has magnetic moment \( \mu_n \). If \( \mu_n\) \( \\\alpha n^x \), the value of \( x \) is:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: [Assume \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( m_e = 9.0 \times 10^{-31} \, \text{kg} \) and \( m_p = 1836 \) times \( m_e \)]

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

The longest wavelength associated with Paschen series is:
(Given \( R_H = 1.097 \times 10^{7} \) SI unit)

The angular momentum of an electron in a hydrogen atom is proportional to: (Where \( r \) is the radius of orbit of electron)

Which figure shows the correct variation of applied potential difference \( V \) with photoelectric current \( I \) at two different intensities of light \( (I_{1} < I_{2}) \) of same wavelengths:

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:

The energy equivalent of \( 1 \) \( \text{g} \) of substance is:

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \( 25\% \) of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

The threshold frequency of a metal with work function \( 6.63 \, \text{eV} \) is:

A nucleus has mass number \( A_{1} \) and volume \( V_{1} \). Another nucleus has mass number \( A_{2} \) and Volume \( V_{2} \). If relation between mass number is \( A_{2} = 4 A_{1} \) then \( \dfrac{V_{2}}{V_{1}} = \) ________.

Radius of a certain orbit of hydrogen atom is 8.48 Å . If energy of electron in this orbit is \( \frac{E}{x} \). then \( x = \) ________.
$(\text{Given } a_0 = 0.529\text{Å}, E = \text{energy of electron in ground state}).$

When a hydrogen atoms going from \( n = 2 \) to \( n = 1 \) emits a photon, its recoil speed is \( \dfrac{x}{5} \, \text{m /s}^{} \). Where \( x = \) ________________. (Use, mass of hydrogen atom \( = 1.6 \times 10^{-27} \, \text{kg} \) )

Two sources of light emit with a power of \( 200 \, \text{W} \). The ratio of number of photons of visible light emitted by each source having wavelengths \( 300 \, \text{nm} \) and \( 500 \, \text{nm} \) respectively, will be:

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number \( 192 \) is:

Binding energy of a certain nucleus is \( 18 \times 10^{8} \, \text{J} \). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Average force exerted on a non-reflecting surface at normal incidence is \( 2.4 \times 10^{-4} \, \text{N} \). If \( 360 \, \text{W}/\text{cm}^{2} \) is the light energy flux during span of \( 1 \) hour \( 30 \) minutes. Then the area of the surface is:

Monochromatic light of frequency \( 6 \times 10^{14}\,\text{Hz} \) is produced by a laser. The power emitted is \( 2 \times 10^{-3}\,\text{W} \). How many photons per second on an average, are emitted by the source?

The radius of third stationary orbit of electron for Bohr's atom is \( R \). The radius of fourth stationary orbit will be:

The mass defect in a particular reaction is \( 0.4 \, \text{g} \). The amount of energy liberated is \( n \times 10^{7} \, \text{kWh} \), where \( n = \_\_\_\_\_\_\_\_ \). (speed of light \( = 3 \times 10^{8} \, \text{m/s} \))

When a metal surface is illuminated by light of wavelength \( \lambda \), the stopping potential is \( 8 \,\text{V} \). When the same surface is illuminated by light of wavelength \( 3\lambda \), stopping potential is \( 2 \,\text{V} \). The threshold wavelength for this surface is:

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JEE Main 2024 27th Jan Morning Shift

The radius of third stationary orbit of electron for Bohr's atom is \( R \). The radius of fourth stationary orbit will be: