Atomic Structure — JEE Advanced PYQs

The 2s and the 2p orbital energies of hydrogen atom are ${\mathrm{E}}_{2\mathrm{s}}(\mathrm{H})$ and ${\mathrm{E}}_{2\mathrm{p}}(\mathrm{H})$, respectively. The 2s and the 2p orbital energies of lithium atom are ${\mathrm{E}}_{2\mathrm{s}}(\mathrm{Li})$ and …

${\mathbf{X}}^{\mathbf{a}+}$ and ${\mathbf{Y}}^{\mathbf{b}+}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=1$ and $n=2$ of ${\mathbf{X}}^{\mathbf{a}+}$ is $\lambda$. The wavelength of light absorb …

Among the following, the correct statement(s) for electrons in an atom is(are)

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

For ${\mathrm{He}}^{+}$, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm.
The wavelength (in nm) of the emitted photon during the transition is ____.
[Use:
Bohr radius, $a=52.9$ pm
Rydberg constant, …

Consider a helium (He) atom that absorbs a photon of wavelength 330 nm . The change in the velocity (in $\mathrm{cm}{\mathrm{s}}^{-1}$ ) of He atom after the photon absorption is ____.
(Assume: Momentum is conserved when photon is absorbed.
Use: Planck constant …

The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state $\Psi$ of ${\mathrm{He}}^{+}$ 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 …

Answer the following by appropriately matching the lists based on the information given in the paragraph

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 $n^{\text{th}}$ orbit …

| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

$P$ 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 $4\pi r^{2}dr$. The qualitative sketch of the dependence of $P$ on $r$ is

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 ${\mathrm{H}}^{-}$is

In an atom, the total number of electrons having quantum numbers $n=4,\left|m_l\right|=1$ and $m_s=-\frac{1}{2}$ 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 $-73^{\circ }C$ is "$M$" times that of the de Broglie wavelength of Ne at $727^{\circ }C$. $M$ is

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_0$ is Bohr radius]

The maximum number of electrons that can have principal quantum number, $n=3$, and spin quantum number, $m_{\mathrm{s}}=-1/2$, is

The work function ( $\varphi$ ) 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
| Metal | Li | Na | K | Mg | Cu | Ag | Fe | Pt | W || --- | --- | --- | --- | --- | --- | --- | --- | - …

The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

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 × 4 matrix given in the ORS.

Column I
(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital
(B) A …