Chapter 4

Which of the following statements is /are correct? (a) The energy of an electron is largely determined by its principal quantum number. (b) The energy of electron in an orbital in the hydrogen atom depends upon the value of principal quantum number only. (c) The value of principal quantum number for \(24^{\text {* }}\) electron is 3 . (d) The principal quantum number is a measure of the most probable distance of finding the electron around the nucleus

The wavelength associated with an electron (mass = \(9.11 \times 10^{-31} \mathrm{~kg}\) ) moving with a velocity of \(10^{6} \mathrm{~m} \mathrm{~s}^{-1}\) is \(\left(\mathrm{h}=6.625 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right)\) (a) \(0.727 \mathrm{~nm}\) (b) \(7.27 \mathrm{~nm}\) (c) \(727 \mathrm{~nm}\) (d) \(7.27 \mathrm{~m}\)

The wavelength associated with an electron (mass = \(9.11 \times 10^{-31} \mathrm{~kg}\) ) moving with a velocity of \(10^{6} \mathrm{~m} \mathrm{~s}^{-1}\) is \(\left(\mathrm{h}=6.625 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right)\) (a) \(0.727 \mathrm{~nm}\) (b) \(7.27 \mathrm{~nm}\) (c) \(727 \mathrm{~nm}\) (d) \(7.27 \mathrm{~m}\)

Particle A moving with a certain velocity has de Broglie wavelength of \(1 \AA\). If the particle B has mass \(20 \%\) and velocity \(80 \%\) of that of \(A\), the de Broglie wavelength of \(\mathrm{B}\) will be

Which of the following ions has magnetic moment equal to that of \(\mathrm{Ti}^{3+}\) (a) \(\mathrm{Ni}^{\mathrm{i}^{+}}\) (b) \(\mathrm{Co}^{2+}\) (c) \(\mathrm{Fe}^{2+}\) (d) \(\mathrm{Cu}^{2+}\)

An ion of a d-block element has magnetic moment 5.92 BM select the ion among the following: (a) \(\mathrm{Sc}^{3+}\) (b) \(\mathrm{Zn}^{2+}\) (c) \(\mathrm{Mn}^{2+}\) (d) \(\mathrm{Cr}^{3+}\)

Match the following Column-I (a) \(2 \mathrm{~s}, 3 \mathrm{~s}, 4 \mathrm{~s}, 4 \mathrm{~d}\) (order of increasing energy) (b) Quantum numbers of \(2 \mathrm{~s}^{2}\) electrons \(\begin{array}{cccc}\mathrm{n} & l & \mathrm{~m} & \mathrm{~s} \\ 2 & 0 & 0 & +1 / 2 \\ 2 & 0 & 0 & -1 / 2\end{array}\)\begin{tabular}{l} (c) \(2 \mathrm{p}^{3}\) is & 1 & 1 & 1 & and \\ \hline \end{tabular} (d) Principal quantum no. \(\mathrm{n}\) Column-II (p) Bohr (q) Hund's rule (r) Pauli's exclusion principle (s) Aufbau principle (t) Size of orbit

Match the following Column-I (a) \(2 \mathrm{~s}\) (b) \(2 \mathrm{p}\) (c) \(3 \mathrm{~s}\) (d) \(3 \mathrm{p}\) Column-II (p) sum of \((\mathrm{n}+1)\) is 3 (q) total number of nodes are two (r) Only one node (s) No radial node (t) No angular node

Match the following Column-I (a) \([\mathrm{Ar}] 3 \mathrm{~d}^{8} 4 \mathrm{~s}^{2}\) (b) \([\mathrm{Ar}] 3 \mathrm{~d}^{10}\) (c) \([\mathrm{Ar}] 3 \mathrm{~d}^{1}\) (d) \([\mathrm{Ar}] 3 \mathrm{~d}^{9}\) Column-II (p) \(\mathrm{Cu}^{2+}\) (q) \(\mathrm{Zn}^{2+}\) (r) \(\mathrm{Ti}^{+3}\) (s) \(\mathrm{Cu}^{+}\) (t) \(\mathrm{Ni}\)

The ground state electronic wave function of hydrogen atom is proportional to \(\mathrm{e}^{-\operatorname{rin}_{0}}\) where \(\mathrm{r}\) is the distance from the nucleus and \(\mathrm{a}_{0}\) is a constant. Calculate the relative probability of finding the electron inside a region of volume \(1.0 \mathrm{pm}^{3}\), located at the nucleus to a distance of \(\mathrm{a}_{0}\) from the nucleus. Report your answer in single digit ignoring any fraction involved. (Given: \(\ln 0.14=-2\) )

The maximum number of \(4 \mathrm{f}\) electrons having spin quantum number \(-1 / 2\) is [2010]

What is the difference in the angular momentum of an electron present in \(2 \mathrm{p}\) and that present in \(4 \mathrm{p}\) orbital?

Find out the number of waves made by a Bohr electron in one complete revolution in its \(3^{\text {nd }}\) orbit?

Calculate the number of nodal planes in the \(\mathrm{d}_{\mathrm{xy}}\) orbital.

Atomic No. of \(\mathrm{Fe}=26\); Number of electrons present in 3 d orbital in \(\mathrm{Fe}^{2+}\) ion is

Due to transition between different energy levels in H-atom, the de-Broglie wavelength of electron is decreased from \(16.5 \AA\) to \(6.6 \AA\). Maximum number of spectral lines that can be observed for these transitions are

Total number of isoelectronic species among the following is \(\mathrm{N}^{3-}, \mathrm{Fe}^{3+}, \mathrm{Al}^{3+}, \mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Zn}^{2+}, \mathrm{F}^{-}, \mathrm{Be}, \mathrm{Na}^{+}, \mathrm{Ne}\)

How many electrons are present in Si atom corresponding to \(l=1\) ?

Uncertainty in position of a particle of \(25 \mathrm{~g}\) in space is \(10^{-5} \mathrm{~m} .\) Hence uncertainty in velocity \(\left(\mathrm{ms}^{-1}\right)\) is (Planck constant \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\) ) \(\quad\) [2002] (a) \(2.1 \times 10^{-28}\) (b) \(2.1 \times 10^{-34}\) (c) \(0.5 \times 10^{-34}\) (d) \(5.0 \times 10^{-24}\)

Uncertainty in position of a particle of \(25 \mathrm{~g}\) in space is \(10^{-5} \mathrm{~m} .\) Hence uncertainty in velocity \(\left(\mathrm{ms}^{-1}\right)\) is (Planck constant \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\) ) \(\quad\) [2002] (a) \(2.1 \times 10^{-28}\) (b) \(2.1 \times 10^{-34}\) (c) \(0.5 \times 10^{-34}\) (d) \(5.0 \times 10^{-24}\)

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen? (a) \(3 \longrightarrow 2\) (b) \(5 \longrightarrow 2\) (c) \(4 \longrightarrow 1\) (d) \(2 \longrightarrow 5\)

The de Broglie wavelength of a tennins ball of mass \(60 \mathrm{~g}\) moving with a velocity of 10 metres per second is approximately \([2003]\) Planck constant \(\mathrm{h}=6.63 \times 10^{-31} \mathrm{Js}\) ) (a) \(10^{-33} \mathrm{~m}\) (b) \(10^{-31} \mathrm{~m}\) (c) \(10-16 \mathrm{~m}\) (d) \(10^{-25} \mathrm{~m}\)

Which one of the following grouping represents a collection of isoelectronic species? (At. numbers \(\mathrm{Cs}-55, \mathrm{Br}-35)\) (a) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}\) (b) \(\mathrm{N}^{3}, \mathrm{~F}^{-} \mathrm{Na}^{+}\) (c) \(\mathrm{Be}, \mathrm{Al}^{3+}, \mathrm{Cl}^{-}\) (d) \(\mathrm{Ca}^{2+}, \mathrm{Cs}^{+}, \mathrm{Br}\)

The number of d electrons retained in \(\mathrm{Fe}^{2+}\) (At. number of \(\mathrm{Fe}=26\) ) ions is (a) 3 (b) 4 (c) 5 (d) 6

Which of the following sets of quantum numbers is correct for an electron in 4f orbital? (a) \(\mathrm{n}=4, l=3, \mathrm{~m}=+4, \mathrm{~s}=+1 / 2\) (b) \(\mathrm{n}=4, l=4, \mathrm{~m}=-4, \mathrm{~s}=-1 / 2\) (c) \(\mathrm{n}=4, l=3, \mathrm{~m}=+\mathrm{l}, \mathrm{s}=+1 / 2\) (d) \(\mathrm{n}=3, l=2, \mathrm{~m}=-2, \mathrm{~s}=+1 / 2\)

The wavelength of the radiation emitted, when in a hydrogen atom electron falls from infinity to station ary state 1 , would be (Rydberg constant \(=1.097 \times 10^{7}\) \(\mathrm{m}^{-1}\) ) \(\quad\) [2004] (a) \(91 \mathrm{~nm}\) (b) \(192 \mathrm{~nm}\) (c) \(406 \mathrm{~nm}\) (d) \(9.1 \times 10^{-8} \mathrm{~nm}\)

Which one of the following sets of ions represents the collection of isoelectronic species? (a) \(\mathrm{K}+\mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Cl}^{-}\) (b) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{F}^{-}\) (c) \(\mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{Mg}^{2+}, \mathrm{Sc}^{3+}\) (d) \(\mathrm{Na}^{+} \mathrm{Mg}^{2+}, \mathrm{Al}^{3+}, \mathrm{Cl}^{-}\)

In a multielectron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic field and electric fields? \(\quad\) [2005] (a) \(\mathrm{n}=1, l=0, \mathrm{~m}=0\) (b) \(\mathrm{n}=2, l=0, \mathrm{~m}=0\) (c) \(\mathrm{n}=3, l=1, \mathrm{~m}=1\) (d) \(\mathrm{n}=3, l=2, \mathrm{~m}=1\) (e) \(\mathrm{n}=3, l=2, \mathrm{~m}=0\) (a) \(\mathrm{b}\) and \(\mathrm{c}\) (b) \(\mathrm{d}\) and \(\mathrm{e}\) (c) \(\mathrm{c}\) and \(\mathrm{d}\) (d) a and \(\mathrm{b}\)

Which of the following statements in relation to the hydrogen atom is correct? \([2005]\) (a) \(3 \mathrm{~s}\) and \(3 \mathrm{p}\) orbitals are of lower energy than \(3 \mathrm{~d}\) orbital (b) 3p orbital is lower in energy than \(3 \mathrm{~d}\) orbital (c) 3 s orbital is lower in energy than \(3 \mathrm{p}\) orbital (d) \(3 \mathrm{~s}, 3 \mathrm{p}\) and \(3 \mathrm{~d}\) orbitals all have the same energy

Of the following sets which one does not contain iso electronic species? (a) \(\mathrm{PO}_{4}^{3-}, \mathrm{SO}_{4}^{2-}, \mathrm{ClO}_{4}^{-}\) (b) \(\mathrm{CN}^{-}, \mathrm{N}_{2}, \mathrm{C}_{2}^{2-}\) (c) \(\mathrm{SO}_{3}^{2-}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3}^{-}\) (d) \(\mathrm{BO}_{3}{\underline{\phantom{xx}}}^{3}, \mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2}-\mathrm{NO}_{3}^{-}\)

According to Bohr theory, the angular momentum of an electron in 5 th orbit is (a) \(25 \mathrm{~h} / \pi\) (b) \(1.0 \mathrm{~h} / \pi\) (c) \(10 \mathrm{~h} / \mathrm{\pi}\) (d) \(2.5 \mathrm{~h} / \pi\)

Which one of the following sets of ions represents a collection of isoelectronic species? (a) \(\mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{Ca}^{2+}, \mathrm{S} \mathrm{c}^{3+}\) (b) \(\mathrm{Ba}^{2+}, \mathrm{Sr}^{2+}, \mathrm{K}^{+}, \mathrm{Ca}^{2+}\) (c) \(\mathrm{N}^{3-}, \mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{S}^{2-}\) (d) \(\mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+} \mathrm{Ca}^{2+}\)

Which of the following sets of quantum numbers represents the highest energy of an atom? [2007] (a) \(\mathrm{n}=3, l=2, m=1, \mathrm{~s}=+1 / 2\) (b) \(\mathrm{n}=4, l=0, \mathrm{~m}=0, \mathrm{~s}=+1 / 2\) (c) \(\mathrm{n}=3, l=0, \mathrm{~m}=0, \mathrm{~s}=+1 / 2\) (d) \(\mathrm{n}=3, l=1, \mathrm{~m}=1, \mathrm{~s}=+1 / 2\)

Which one of the following constitutes a group of the isoelectronic species? (a) \(\mathrm{C}_{2}^{2-}, \mathrm{O}_{2}^{-}, \mathrm{CO}, \mathrm{NO}\) (b) \(\mathrm{NO}^{+}, \mathrm{C}_{2}^{2}, \mathrm{C}^{\mathrm{N}-}, \mathrm{N}_{2}\) (c) \(\mathrm{CN}^{-}, \mathrm{N} 2, \mathrm{O}_{2}^{2-}, \mathrm{C}_{2}^{2-}\) (d) \(\mathrm{N}_{2}, \mathrm{O}_{2}^{-}, \mathrm{NO}^{+}, \mathrm{CO}\)

In an atom, an electron is moving with a speed of \(600 \mathrm{~m} / \mathrm{s}\) with an accuracy of \(0.005 \%\). Certainity with which the position of the electron can be located is \(\left(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\right.\), mass of electron, \(\mathrm{em}=9.1 \mathrm{x}\) \(\left.10^{-31} \mathrm{~kg}\right)\) [2009] (a) \(5.10 \times 10^{-3} \mathrm{~m}\) (b) \(1.92 \times 10^{-3} \mathrm{~m}\) (c) \(3.84 \times 10^{-3} \mathrm{~m}\) (d) \(1.52 \times 10^{-3} \mathrm{~m}\)

Calculate the wavelength (in monometer) associated with a proton moving at \(1.0 \times 10^{3} \mathrm{~ms}^{-1}\) (Mass of proton \(=1.67 \times 10^{-27} \mathrm{~kg}\) and \(\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right): \quad[\mathbf{2 0 0 9}]\) (a) \(0.40 \mathrm{~nm}\) (b) \(2.5 \mathrm{~nm}\) (c) \(14.0 \mathrm{~nm}\) (d) \(0.032 \mathrm{~nm}\)

A gas adsorbs a photon of \(355 \mathrm{~nm}\) and emits at two wavelengths. If one of the emissions is at \(680 \mathrm{~nm}\), the other is at: (a) \(743 \mathrm{~nm}\) (b) \(376 \mathrm{~nm}\) (c) \(453 \mathrm{~nm}\) (d) \(581 \mathrm{~nm}\)

The electrons identified by quantum numbers \(\mathrm{n}\) and \(l\) \([\mathbf{2 0 1 2}]\) (1) \(\mathrm{n}=4, l=0\) (2) \(\mathrm{n}=4, l=1\) (3) \(\mathrm{n}=3, l=1\) (4) \(\mathrm{n}=3, l=2\) can be placed in order of increasing energy as (a) \(4<2<3<1\) (b) \(2<4<1<3\) (c) \(1<3<2<4\) (d) \(3<4<2<1\)

Energy of an electron is given by, [2013] \(\mathrm{E}=-2.178 \times 10^{-18}\left(\frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}}\right)\) Wavelength of light required to excite an electron in an hydrogen atom from level \(\mathrm{n}=1\) to \(\mathrm{n}=2\) will be \(\left(\mathrm{h}=6.62 \times 10^{-34} \mathrm{Js}\right.\) and \(\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)\)Energy of an electron is given by, [2013] \(\mathrm{E}=-2.178 \times 10^{-18}\left(\frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}}\right)\) Wavelength of light required to excite an electron in an hydrogen atom from level \(\mathrm{n}=1\) to \(\mathrm{n}=2\) will be \(\left(\mathrm{h}=6.62 \times 10^{-34} \mathrm{Js}\right.\) and \(\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)\)

The correct set of four quantum numbers for the valence electrons of rubidium atom \((\mathrm{Z}=37)\) is: [2014] (a) \(5,1,1, \frac{1}{2}\) (b) \(5,0,1, \frac{1}{2}\) (c) \(5,0,0, \frac{1}{2}\) (d) \(5,1,0, \frac{1}{2}\)

Which of the following is the energy of a possible excited state of hydrogen? [2015] (a) \(+13.6 \mathrm{eV}\) (b) \(-6.8 \mathrm{eV}\) (c) \(-3.4 \mathrm{eV}\) (d) \(+6.8 \mathrm{eV}\)

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference \(\mathrm{V}\) esu. If e and \(\mathrm{m}\) are charge and mass of an electron, respectively, then the value of \(\mathrm{h} / \lambda\) (where \(\lambda\) is wavelength associated with electron wave) is given by: \([2016]\) (a) \(2 \mathrm{meV}\) (b) \(\sqrt{\mathrm{meV}}\) (c) \(\sqrt{2 \mathrm{meV}}\) (d) meV