Atomic Structure

The wavelength of an electron and a neutron will become equal when the velocity of the electron is $x$ times the velocity of neutron. The value of $x$ is ______. (Nearest Integer)

(Mass of electron is $9.1\times10^{-31}$ kg and mass of neutron is $1.6\times10^{-27}$ kg)

Consider an imaginary ion ${}^{48}_{22}\mathrm X^{3-}$. The nucleus contains 'a'% more neutrons than the number of electrons in the ion. The value of 'a' is ______. [nearest integer]

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.

Reason R: Energies of the orbitals in the same subshell decrease with increase in the atomic number.

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

The correct decreasing order of energy for the orbitals having, following set of quantum numbers :

(A) n = 3, l = 0, m = 0
(B) n = 4, l = 0, m = 0
(C) n = 3, l = 1, m = 0
(D) n = 3, l = 2, m = 1

is :

Identify the incorrect statement from the following.

If the wavelength for an electron emitted from H-atom is $3.3\times10^{-10}$ m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is ______ times. (Nearest integer)

[Given : h = $6.626\times10^{-34}$ J s]

Mass of electron = $9.1\times10^{-31}$ kg

The minimum uncertainty in the speed of an electron in an one dimensional region of length 2a$_0$ (Where a$_0$ = Bohr radius 52.9 pm) is _______ km s$^{-1}$.

(Given : Mass of electron = $9.1\times10^{-31}$ kg, Planck's constant h = $6.63\times10^{-34}$ Js)

Given below are the quantum numbers for 4 electrons.

A. n = 3, l = 2, m$_l$ = 1, m$_s$ = +1/2
B. n = 4, l = 1, m$_l$ = 0, m$_s$ = +1/2
C. n = 4, l = 2, m$_l$ = −2, m$_s$ = −1/2
D. n = 3, l = 1, m$_l$ = −1, m$_s$ = +1/2

The correct order of increasing energy is

When the kinetic energy of an electron is increased nine times, the wavelength of the de-Broglie wave associated with it would become :

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 $= 6 \times 10^{23}$ mol$^{-1}$, Molar mass of He $= 4$ g mol$^{-1}$)

A proton and a Li$^{3+}$ nucleus are accelerated by the same potential. If λ$_{Li}$ and λ$_p$ denote the de Broglie wavelengths of Li$^{3+}$ and proton respectively, then the value of $\dfrac{\lambda_{Li}}{\lambda_p}$ is $x\times10^{-1}$. The value of $x$ is _______. (Rounded off to the nearest integer)

[Mass of Li$^{3+}$ = 8.3 mass of proton]

The figure below is the plot of potential energy versus internuclear distance $(d)$ of $\ce{H2}$ molecule in the electronic ground state. What is the value of the net potential energy $E_0$ (as indicated in the figure) in $\mathrm{kJ\,mol^{-1}}$, for $d = d_0$ 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 $6.023\times10^{23}\ \mathrm{mol^{-1}}$.

The ground state energy of hydrogen atom is −13.6 eV. Consider an electronic state $\Psi$ of $\ce{He+}$ 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 $\Psi$?

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

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

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

For hydrogen atom, the only CORRECT combination is

For $\ce{He+}$ ion, the only INCORRECT combination is

The radius of the second Bohr orbit for hydrogen atom is :

(Planck's Const. $h=6.6262\times10^{-34}$ Js; mass of electron $=9.1091\times10^{-31}$ kg; charge of electron $e=1.60210\times10^{-19}$ C; permittivity of vacuum $\epsilon_0=8.854185\times10^{-12}$ kg$^{-1}$m$^{-3}$A$^2$)

If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of $\ce{He+}$ is :