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Bohr's Model and Physics of the Atom — JEE Main & Advanced Physics PYQs

83 previous year questions from Bohr's Model and Physics of the Atom with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

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1

The Bohr radius is given by a₀ = ₀ h^2 m e^2 . Determine the dimensions of the right-hand side.

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Determine the wavelength of the radiation emitted by hydrogen during the transition from n = 10 to n = 9 .

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Determine the smallest wavelength of radiation that can be emitted by hydrogen.

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Determine the wavelength of the radiation emitted by hydrogen during the transition from n = 3 to n = 2 .

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Determine the wavelength of the radiation emitted by hydrogen during the transition from n = 5 to n = 4 .

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Determine the smallest wavelength of radiation that can be emitted by He ^+ .

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Determine the smallest wavelength of radiation that can be emitted by Li ⁺⁺ .

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Calculate the Rydberg constant by substituting the values of the fundamental constants into its expression.

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Determine the binding energy of a hydrogen atom when it is in the n = 2 state.

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Determine the radius and energy of a He ^+ ion in the state n = 1 .

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Determine the radius and energy of a He ^+ ion in the state n = 4 .

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Determine the radius and energy of a He ^+ ion in the state n = 10 .

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Determine the first excitation potential for a He ^+ ion.

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A hydrogen atom emits ultraviolet radiation having a wavelength of 102.5 nm . Determine the quantum numbers of the states involved in the transition.

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Determine the ionization potential for a Li ⁺⁺ ion.

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A collection of hydrogen atoms is prepared in the n = 4 state. Identify the wavelengths of the radiation emitted as the atoms make transitions and return to the n = 2 state.

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A positive ion with exactly one electron ejects this electron when it absorbs a photon of wavelength 228 Å or shorter. Determine the ion.

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Determine the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.

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A hydrogen atom in a state with a binding energy of 0.85 eV undergoes a transition to a state having an excitation energy of 10.2 eV . Determine the quantum numbers n of the upper

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A hydrogen atom in a state with a binding energy of 0.85 eV undergoes a transition to a state having an excitation energy of 10.2 eV . Calculate the wavelength of the emitted radia

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Every time hydrogen emits a photon in the Balmer series, it is followed by another photon in the Lyman series. Find the wavelength corresponding to this latter photon.

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A hydrogen atom initially in the n = 6 state undergoes two successive transitions to reach the ground state. During the first transition, a photon of 1.13 eV is emitted. Determine

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A hydrogen atom initially in the n = 6 state undergoes two successive transitions to reach the ground state. During the first transition, a photon of 1.13 eV is emitted. What is th

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Determine the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state.

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A hot gas emits radiation exclusively at wavelengths of 46.0 nm , 82.8 nm , and 103.5 nm . Assume the atoms possess only two excited states, and the energy difference between conse

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A gas of hydrogen-like ions is prepared in a specific excited state A . It subsequently emits photons that have a wavelength equal to the wavelength of the first line of the Lyman

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Determine the maximum angular speed of the electron in a stationary orbit of a hydrogen atom.

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A spectroscopic instrument is capable of resolving two closely spaced wavelengths, and + , provided that the ratio / is smaller than 8000 . This instrument is employed to examine t

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Assume that under specific conditions, hydrogen atoms are permitted to undergo only those transitions where the principal quantum number n changes by 2 . Determine the smallest wav

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Assume that under specific conditions, hydrogen atoms are permitted to undergo only those transitions where the principal quantum number n changes by 2 . Determine the wavelength(s

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Based on Maxwell's theory of electrodynamics, an electron travelling in a circle ought to emit radiation with a frequency equal to its frequency of revolution. If this rule is appl

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At a temperature T , the average kinetic energy of gas molecules is given by 1.5 kT . Determine the temperature at which the average kinetic energy of hydrogen molecules equals the

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Determine the temperature at which the average thermal kinetic energy matches the energy required to excite a hydrogen atom from its ground state to the n = 3 state. Hydrogen can s

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For a hydrogen atom excited to the n = 2 state, the average lifetime is 10⁻⁸ ext s . Determine the average number of revolutions completed by the electron before it transitions to

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For hydrogen-like atoms and ions, the ratio of the magnetic dipole moment to the angular momentum ( l = m v r ) is a universal constant. Determine the value of this constant.

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A light beam with wavelengths distributed uniformly between 450 nm and 550 nm is passed through a sample of hydrogen gas. Which wavelength will exhibit the least intensity in the t

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Radiation emitted from the n = 2 to n = 1 transition of hydrogen atoms is incident on helium ions that are in the n = 1 and n = 2 states. Determine the possible transitions of the

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Determine the magnetic dipole moment associated with the motion of the electron in a hydrogen atom's ground state.

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A hydrogen atom in the ground state absorbs an ultraviolet radiation photon of wavelength 50 nm . Assuming the entire photon energy is taken up by the electron, determine the kinet

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A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in the ground state. Assume that when a photon supplies a portion of its energy to a hy

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A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in the ground state. Assume that when a photon supplies a portion of its energy to a hy

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Photoelectrons are ejected from a cesium surface ( = 1.9 eV ) by a beam of monochromatic light of wavelength . These photoelectrons are subsequently directed to collide with hydrog

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A beam of monochromatic light of wavelength is used to eject photoelectrons from a cesium surface ( = 1.9 eV ). The ejected photoelectrons are then made to collide with ground-stat

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Monochromatic light of wavelength ejects photoelectrons from a cesium surface having a work function of = 1.9 eV . These photoelectrons are made to collide with hydrogen atoms init

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Emitted from an electron gun with almost zero velocity, electrons are accelerated by an electric field E over a distance of 1.0 m . These electrons are subsequently scattered by a

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A neutron with a kinetic energy of 12.5 eV strikes a stationary hydrogen atom. Neglecting the mass difference between the neutron and the hydrogen atom, and assuming the neutron's

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A hydrogen atom travelling at a speed v collides with a stationary hydrogen atom. Determine the minimum value of v such that one of the atoms could become ionized. The mass of a hy

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Travelling with a speed v , a neutron strikes a hydrogen atom in the ground state that is moving towards it with the same speed. Determine the minimum speed of the neutron for whic

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When a photon is emitted by a hydrogen atom, it carries momentum. Calculate the momentum carried by the photon if a hydrogen atom emits light of wavelength 656.3 nm .

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When a photon is emitted by a hydrogen atom, it carries momentum. A hydrogen atom emits light of wavelength 656.3 nm . Determine the speed at which the atom recoils during this tra

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When a photon is emitted by a hydrogen atom, it carries momentum. A hydrogen atom emits light of wavelength 656.3 nm . Find the kinetic energy of recoil of the atom. Take the mass

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The light emitted during the transition from n = 3 to n = 2 in hydrogen is known as H_ light. Determine the maximum work function a metal can possess such that this H_ light is cap

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An atom recoils when it emits a photon. The energy of the photon and the recoil kinetic energy are derived from the energy difference between the states involved in the transition.

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Radiation emitted from a hydrogen discharge tube is incident on a cesium plate. Determine the maximum possible kinetic energy of the emitted photoelectrons. The work function of ce

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Due to gravitational attraction, the earth revolves round the sun. Assume that the sun and the earth are point particles with their existing masses, and that Bohr's quantization ru

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Light from the Balmer series of hydrogen is capable of ejecting photoelectrons from a metal. Determine the maximum possible work function of the metal.

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Due to gravitational attraction, the earth revolves round the sun. Assume that the sun and the earth are point particles with their existing masses, and that Bohr's quantization ru

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Imagine a neutron and an electron bound to each other by gravitational force. Assuming Bohr's quantization rule for angular momentum is applicable in this scenario, determine the e

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A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum

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Radiation from a hydrogen-discharge tube passes through a filter that transmits only wavelengths greater than 440 nm . This transmitted radiation is then incident on a metal with a

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A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum

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Imagine a hypothetical world where angular momentum is quantized as even integral multiples of h/2 . Based on Bohr's model, what would be the longest possible wavelength emitted by

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An excited hydrogen atom in state n travels with a velocity v ( v c ). It emits a photon in the direction of its motion and transitions to a lower state m . Applying the principles

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A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum

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Three photons originating from an excited atomic-hydrogen sample are detected. Their energies are 12.1 eV , 10.2 eV , and 1.9 eV . These photons must have been emitted by

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Among the following transitions, which one results in the minimum wavelength?

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Among the following systems, which will have the minimum radius for the first orbit ( n = 1 )?

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For an electron in a hydrogen atom, the minimum orbital angular momentum is given by

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Assume an electron in a hydrogen atom undergoes a transition from n = 3 to n = 2 in 10⁻⁸ s . Using the standard relation between torque and angular momentum, the order of magnitude

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For which of the following systems is the wavelength associated with the transition from n = 2 to n = 1 the minimum?

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Identify the curve from the figure below that could depict the speed of an electron in a hydrogen atom as a function of its principal quantum number n .

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In a one-electron system, the radius of the shortest orbit is given as 18 pm . This system could be

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When a hydrogen atom in the ground state absorbs 10.2 eV of energy, the orbital angular momentum of the electron increases by

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For all hydrogen-like atoms and ions in their ground states, which of the following parameters is identical?

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As higher values of n are considered for orbits in a hydrogen atom, the electric potential energy of the atom

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Within a laser tube, every photon

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An atom (or ion) has a ground state energy of -54.4 eV . This species could be

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During a laboratory experiment involving emission from atomic hydrogen in a discharge tube, only a small number of lines are observed, while the hydrogen spectrum of a star exhibit

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In a hydrogen atom, which of the following products do not depend on the principal quantum number n ? The symbols carry their standard meanings.

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An electron possessing a kinetic energy of 5 eV strikes a hydrogen atom in its ground state. The collision

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When a photon stimulates the emission of another photon, both photons possess

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Suppose the ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B . Let r , u , E , and L denote the orbit radius, electron speed, atom ene

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Suppose A_n represents the area enclosed by the n th orbit of a hydrogen atom. A plot of (A_n/A₁) versus (n)

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