Structure of Atom · Chemistry · JEE Advanced

According to Bohr's model, the highest kinetic energy is associated with the electron in the

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n.


Which of the following options has the correct combination considering List-I and List-II?

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n.


Which of the following options has the correct combination considering List-I and List-II?

For $$H{e^ + }$$ ion, the only INCORRECT combination is

For hydrogen atom, the only CORRECT combination is :

For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is :

P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is $$4\pi r^2dr$$. The quantitative ketch of the dependence of P on r is

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$$\alpha_0$$ is Bohr radius]

The hydrogen like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

The state S₁ is :

The hydrogen like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

Energy of the state S₁ in units of the hydrogen atom ground state energy is:

The hydrogen like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

The orbital angular momentum quantum number of the state S₂ is

Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

	Column I		Column II
(A)	Orbital angular momentum of the electron in a hydrogen-like atomic orbital.	(P)	Principal quantum number
(B)	A hydrogen-like one-electron wave function obeying Pauli's principle.	(Q)	Azimuthal quantum number
(C)	Shape, size and orientation of hydrogen like atomic orbitals.	(R)	Magnetic quantum number
(D)	Probability density of electron at the nucleus in hydrogen-like atom.	(S)	Electron spin quantum number

STATEMENT - 1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45^o slope as the atomic number is increased.


STATEMENT - 2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides

According to Bohr's theory
E_n = Total energy, K_n = Kinetic Energy, V_n = Potential Energy, r_n = Radius of n^th orbit
Match the following

Column I

(A) V_n/K_n = ?
(B) If radius of n^th orbit $$ \propto E_n^x,x = ?$$
(C) Angular momentum in lowest orbital
(D) $${1 \over {{r_n}}} \propto {Z^y},y = ?$$

Column II

(p) 0
(q) -1
(r) -2
(s) 1

The number of radial nodes of 3s and 2p orbitals are respectively

The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom?

Which of the following pairs are isoelectronic and isostructural?
$$NO_3^-$$, $$CO_3^{2-}$$, $$ClO_3^-$$, SO₃

If the nitrogen atom has electronic configuration 1s⁷, it would have energy lower than that of the normal ground state configuration 1s²2s²2p³, because the electrons would be closer to the nucleus. Yet 1s⁷ is not observed because it violates

Rutherford's experiment, which established the nuclear model of the atom, used a beam of

The quantum numbers +1/2 and -1/2 for the electron spin represent

The wavelength associated with a golf ball weighing 200 g and moving at speed of 5 m/h is of the order

The number of nodal planes in a p_x orbital is

The electronic configuration of an element is 1s², 2s² 2p⁶, 3s² 3p⁶ 3d⁵, 4s¹ This represents its

The electrons, identified by quantum numbers n and l, (i) n = 4, l = 1, (ii) n = 4, l = 0, (iii) n = 3, l = 2 and (iv) n = 3, l = 1 can be placed in order of increasing energy, from the lowest to highest, as

ASSERTION:
Nuclide $${}_{13}^{30}Al$$ is less stable than $${}_{20}^{40}Ca$$

REASON:
Nuclides having odd number of protons and neutrons are generally unstable.

The orbital diagram in which the Aufbau principle is violated is

For a d-electron the orbital angular momentum is

The orbital angular momentum of an electron in 2s orbital is

A 3p orbital has

Which of the following does not characterise X-rays?

Which of the following relates to photons both as wave motion and as a stream of particles?

The correct set of quantum numbers for the unpaired electron of chlorine atom is

The correct ground state electronic configuration of chromium atom is

The outermost electronic configuration of the most electronegative element is

The wavelength of a spectral line for an electronic transition is inversely related to :

The triad of nuclei that is isotonic is

The sum of the number of neutrons and proton in the isotope of hydrogen is

Rutherford's alpha particle scattering experiment eventually led to the conclusion that:

Which one of the following sets of quantum numbers represents an impossible arrangement?

The ratio of the energy of a photon of 2000Å wavelength to that 4000Å radiation is

Bohr Model can explain

The radius of an atomic nucleus is of the order of

Electromangnetic radiation with maximum wavelength is:

Which electronic level would allow the hydrogen atom to absorb a photon but not to emit a photon?

The increasing order (lowest first) for the values of e/m (charges/mass) for electron (e), proton (p), neutron (n) and alpha particle ($$\alpha$$) is:

Correct set of four quantum numbers for the valence (outermost) electron of rubidium (Z = 37) is

Rutherford's scattering experiment is related to the size of the

Any p-orbital can accommodate upto

The principal quantum number of an atom is related to the

The ion that is isoelectronic with CO is

Rutherford's experiment on scattering of $$\alpha-particles$$ showed for the first time that the atom has

The number of neutrons in dipositive zinc ion with mass number 70 is

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2 p_{z}$ orbitals is(are)

The ground state energy of hydrogen atom is $$-$$13.6 eV. Consider an electronic state $$\psi $$ of He⁺ whose energy, azimuthal quantum number and magnetic quantum number are $$-$$3.4 eV, 2 and 0, respectively.

Which of the following statement(s) is(are) true for the state $$\psi $$?

Ground state electronic configuration of nitrogen atom can be represented by

Which of the following statement(s) is (are) correct?

Decrease in atomic number is observed during

The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The possible energy value(s) of the excited state(s) for electrons in Bohr orbits of hydrogen is (are)

When alpha particles are sent through a thin metal foil, most of them go straight through the foil because

An isotone of $${}_{32}^{76}Ge$$ is

Many elements have non-integral atomic masses because:

For $\mathrm{He}^{+}$, a transition takes place from the orbit of radius $105.8 \mathrm{pm}$ to the orbit of radius $26.45 \mathrm{pm}$. The wavelength (in nm) of the emitted photon during the transition is _______.

[Use :

Bohr radius, $\mathrm{a}=52.9 \mathrm{pm}$

Rydberg constant, $R_{\mathrm{H}}=2.2 \times 10^{-18} \mathrm{~J}$

Planck's constant, $\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$

Speed of light, $\mathrm{c}=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$ ]

Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s^$$-$$1) of He atom after the photon absorption is __________.

(Assume : Momentum is conserved when photon is absorbed.

Use : Planck constant = 6.6 $$\times$$ 10^$$-$$34 J s, Avogadro number = 6 $$\times$$ 10²³ mol^$$-$$1, Molar mass of He = 4 g mol^$$-$$1)

The figure below is the plot of potential energy versus internuclear distance (d) of H₂ molecule in the electronic ground state. What is the value of the net potential energy E₀ (as indicated in the figure) in kJ mol^-1, for d = d₀ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as 6.023 $$ \times $$ 10²³ mol^-1.

Not considering the electronic spin, the degeneracy of the second excited state( n = 3) of H atom is 9, while the degeneracy of the second excited state of H^– is ___________.

In an atom, the total number of electrons having quantum numbers n = 4, |m_l| = 1 and m_s = –1/2 is

The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at –73^oC is “M” times that of the de Broglie wavelength of Ne at 727^oC. M is

The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, m_s = − 1/2 , is

The work function ( φ ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

Find out the number of waves made by a Bohr electron in once complete revolution in its 3rd orbit?

What is the maximum number of electrons that may be present in all atomic orbitals with principal quantum number 3 and azimuthal quantum number 2?

Find the velocity (ms^-1) of electron in first Bohr's orbit of radius a₀. Also find the de Broglie's wavelength (in m). Find the orbital angular momentum of 2p orbital of hydrogen atom in units of $$h/2 \pi$$.

A ball of mass 100 g is moving with 100 ms^-1. Find it's wavelength.

(a) The Schrodinger wave equation for hydrogen atom is

$$$\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}} \right)^{3/2}}\left( {2 - {{{r_0}} \over {{a_0}}}} \right){e^{ - {r_0}/{a_0}}}$$$
Where a₀ is Bohr's radius. If the radial node in 2s be at r₀, then find r₀ in terms of a₀.

(b) A baseball having mass 100 g moves with velocity 100 m/s. Determine the value of wavelength of baseball.

Wavelength of high energy transition of H-atoms is 91.2 nm. Calculate the corresponding wavelength of He atoms.

Calculate the energy required to excite one litre of hydrogen gas at 1 atm and 298 K to the first excited state of atomic hydrogen. The energy for the dissociation of H-H bond 436 kJ mol^-1.

Calculate the wave number for the shortest wavelength transition in the Balmer series of atomic hydrogen.

Consider the hydrogen atom to be a proton embedded in a cavity of radius a₀ (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in it's ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy.

Iodine molecule dissociates into atoms after absorbing light of 4500 Å. If one quantum of radiation is absorbed by each molecule, calculate the kinetic energy of iodine atoms. (Bond energy of I₂ = 240 kJ mol^-1)

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He⁺ spectrum?

Estimate the difference in energy between 1st and 2nd Bohr orbit for a hydrogen atom. At what minimum atomic number, a transition from n = 2 to n = 1 energy level would result in the emission of X-rays with $$\lambda = 3.0 \times {10^{ - 8}}$$? Which hydrogen atom like species does this atomic number correspond to?

According to Bohr's theory, the electronic energy of hydrogen atom in the n^th Bohr's orbit is given by $${E_n} = {{ - 21.6 \times {{10}^{ - 19}}} \over {{n^2}}}J$$. Calculate the longest wavelength of light (in Å) that will be needed to remove an electron from the third Bohr orbit of the He⁺ ion.

Give reasons why the ground state outermost electronic configuration of silicon is:

The electron energy in hydrogen atom is given by E = (-21.7 $$\times$$ 10^-12)/n² ergs. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength (in cm) of light that can be used to cause this transition?

Calculate the wavelength in Angstrom of the photon that is emitted when an electron in the Bohr orbit, n = 2 returns to the orbit, n = 1 in the hydrogen atom. The ionization potential of the ground state hydrogen atom is 2.17 $$\times$$ 10^-11 erg per atom.

The energy of the electron in the second and the third Bohr's orbits of the hydrogen atom is -5.42 $$\times$$ 10^-12 erg and -2.41 $$\times$$ 10^-12 erg respectively. Calculate the wavelength (in Å) of the emitted radiation when the electron drops from the third to second orbit.

The outermost electronic configuration of Cr is _______.

The 2p_x, 2p_y and 2p_z orbitals of atom have identical shapes but differ in their _____.

Wave functions of electrons in atoms and molecules are called ______.

The light radiations with discrete quantities of energy are called ______.

The uncertainty principle and the concept of wave nature of matter were proposed by ______ and ______ respectively. (Heisenberg Schrodinger, Maxwell, de Broglie)

Elements of the same mass number but of different atomic numbers are known as ____.

Isotopes of an element differ in the number of ______ in their nuclei.

When there are two electrons in the same orbital, they have _____ spins.

The mass of a hydrogen atom is ______ kg.

In a given electric field, $$\beta-particles $$ are deflected more than $$\alpha-particles$$ in spite of $$\alpha-particles$$ having larger charge.

The electron density in the XY plane in 3d_{x² - y²} orbital is zero

Gamma rays are electromagnetic radiations of wavelengths of 10^-6 to 10^-5 cm

The energy of the electron in the 3d-orbital is less than that in the 4s-orbital in the hydrogen atom.

The outer electronic configuration of the ground state chromium atom is 3d⁴ 4s²