Chapter 4

Pick out the wrong statements. (a) \(\mathrm{Fe}^{3+}\) ion is more stable than \(\mathrm{Fe}^{2+}\) ion in the gaseous state. (b) For an electron in a \(4 \mathrm{p}\)-orbital, the quantum numbers are \(\mathrm{n}=4, l=1, \mathrm{~m}=2, \mathrm{~s}=+1 / 2\) (c) Angular momentum of 3 s electron is one. (d) \((\mathrm{n}+l)\) rule is followed for determining the orbital of the lowest energy state.

Which of the following statement is/ are correct? (a) The number of unpaired electrons in both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Mn}^{2+}\) are five. (b) In silver atom, 23 electrons have a spin of one type and 24 of the opposite (atomic number of \(\mathrm{Ag}=\) 47). (c) The azimuthal quantum number may have a negative value. (d) The electronic configuration of \(\mathrm{Cr}\) is \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{\mathrm{l}}\) (atomic number of \(\mathrm{Cr}=24\) )

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 \(24^{\text {t }}\) 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 de Broglie wave length of a moving particle of mass \(1 \mathrm{~g}\) is \(6.625 \times 10^{-23} \mathrm{~m}\). The velocity of the particle is (a) \(100 \mathrm{~cm} \mathrm{~s}^{-1}\) (b) \(100 \mathrm{~m} \mathrm{~s}^{-1}\) (c) \(10 \mathrm{~m} \mathrm{~s}^{-1}\) (d) \(1000 \mathrm{~m} \mathrm{~s}^{-1}\)

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 \(\mathrm{A}\), the de Broglie wavelength of \(\mathrm{B}\) will be (a) \(1.6 \AA\) (b) \(16 \AA\) (c) \(4.0 \AA\) (d) \(6.25 \AA\)

Which of the following ions has the highest magnetic moment? (a) \(\mathrm{Fe}^{2+}\) (b) \(\mathrm{Mn}^{2+}\) (c) \(\mathrm{Cr}^{3+}\) (d) \(\mathrm{V}^{3+}\)

Which of the following ions has magnetic moment equal to that of \(\mathrm{Ti}^{3+}\) (a) \(\mathrm{Ni}^{2+}\) (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 List I with List II and select the correct answer using the codes given below the lists: List-I (Metal ions) ]. \(\mathrm{Cr}^{3+}\) 2\. \(\mathrm{Fe}^{2+}\) 3\. \(\mathrm{Ni}^{2+}\) 4\. \(\mathrm{Mn}^{2+}\) List-II (Magnetic moment) (i) \(\sqrt{35}\) (ii) \(\sqrt{30}\) (iii) \(\sqrt{24}\) (iv) \(\sqrt{15}\) (v) \(\sqrt{8}\)

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 \(\begin{array}{cccc}\mathrm{n} & l & \mathrm{~m} & \mathrm{~s} \\ 2 & 0 & 0 & +1 / 2 \\ 2 & 0 & 0 & -1 / 2\end{array}\) 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

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

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 \(3^{\text {rd }}\) orbit?

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

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

Hydrogen atoms in the ground state are excited by means of monochromatic radiation of wavelength \(970.6 \AA\). How many different lines are possible in the resulting emission spectrum?

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

An ion \(\mathrm{Mn}^{a+}\) has the magnetic moment equal to \(4.9\) B.M. Find the value of a

Energy of H-atom in the ground state is \(-3.6 \mathrm{eV}\), hence energy in the second excited state is (a) \(-6.8 \mathrm{eV}\) (b) \(-3.4 \mathrm{eV}\) (c) \(-1.51 \mathrm{eV}\) (d) \(-4.53 \mathrm{eV}\)

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 \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\) ) \(\quad\) (a) \(2.1 \times 10^{-2 \mathrm{~s}}\) (b) \(2.1 \times 10^{-34}\) (c) \(0.5 \times 10^{-34}\) (d) \(5.0 \times 10^{-24}\)

Which of the following ions has the maximum magnetic moment? \(\quad\) (a) \(\mathrm{Mn}^{2+}\) (b) \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{Ti}^{2+}\) (d) \(\mathrm{Cr}^{2+}\)

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 \(\mathbf\) (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 \(4 \mathrm{f}\) 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) \(\mathrm{n}=4, l=3, \mathrm{~m}=+1, \mathrm{~s}=+1 / 2\) (d) \(\mathrm{n}=3, l=2, \mathrm{~m}=-2, \mathrm{~s}=+1 / 2\)

Consider the ground state of \(\mathrm{Cr}\) atom \((\mathrm{Z}=24)\). The numbers of electrons with the azimuthal quantum numbers, \(l=1\) and 2 are, respectively \(\quad\) (a) 12 and 4 (b) 12 and 5 (c) 16 and 4 (d) 16 and 5

The wavelength of the radiation emitted, when in a hydrogen atom electron falls from infinity to station ary state 1 , would be (Rydberg constant \(=1.097 \times 10^{7}\) \(\left.\mathrm{m}^{-1}\right)\) (a) 9 lnm (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) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{S} \mathrm{c}^{3+}, \mathrm{F}^{-}\) (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? (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? (a) \(3 \mathrm{~s}\) and \(3 \mathrm{p}\) orbitals are of lower energy than \(3 \mathrm{~d}\) orbital (b) \(3 \mathrm{p}\) 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) \(\mathrm{BO}_{3}^{3-}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3}^{-}\)

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) \(10 \mathrm{~h} / \pi\) (d) \(2.5 \mathrm{~h} / \pi\)

Which one of the following sets of ions represents a collection of isoelectronic species? (a) \(\mathrm{K}^{+} \cdot \mathrm{Cl}^{-}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}\) (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? \(\quad\) (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? \(\quad\) (a) \(\mathrm{C}_{2}^{2-}, \mathrm{O}_{2}^{-}, \mathrm{CO}, \mathrm{NO}\) (b) \(\mathrm{NO}^{+}, \mathrm{C}^{2}{\underline{\phantom{xx}}}_{2}, \mathrm{C}^{\mathrm{N}-}, \mathrm{N}_{2}\) (c) \(\mathrm{CN}^{-}, \mathrm{N} 2, \mathrm{O}_{2}^{2-}, \mathrm{C}_{2}^{\frac{2}{2}}\) (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, \(\mathrm{em}=9.1 \mathrm{x}\) \(\left.10^{-31} \mathrm{~kg}\right):\) (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 \(\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right): \quad[\mathbf]\) (a) \(0.40 \mathrm{~nm}\) (b) \(2.5 \mathrm{~nm}\) (c) \(14.0 \mathrm{~nm}\) (d) \(0.032 \mathrm{~nm}\)

The energy required to break one mole of \(\mathrm{Cl}-\mathrm{Cl}\) bonds in \(\mathrm{C}_{12}\) is \(242 \mathrm{~kJ} \mathrm{~mol}^{-1}\). the longest wavelength of light capable of breaking a single \(\mathrm{Cl}-\mathrm{Cl}\) bond is \(\left(\mathrm{c}=3 \times 10^{5} \mathrm{~ms}^{-1}\right.\) and \(\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1} \quad[\mathbf{]\) (a) \(594 \mathrm{~nm}\) (b) \(640 \mathrm{~nm}\) (c) \(700 \mathrm{~nm}\) (d) \(494 \mathrm{~nm}\)

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 \(l\) (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, \(\mathrm{E}=-2.178 \times 10^{-18}\left(\frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}}\right)\) 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 \(\left.\mathrm{c}=3.0 \times 10^{\mathrm{s}} \mathrm{ms}^{-1}\right)\) (a) \(6.500 \times 10^{-7} \mathrm{~m}\) (b) \(8.500 \times 10^{-7} \mathrm{~m}\) (c) \(1.214 \times 10^{-7} \mathrm{~m}\) (d) \(2.816 \times 10^{-7} \mathrm{~m}\)

The correct set of four quantum numbers for the valence electrons of rubidium atom \((\mathrm{Z}=37)\) is: (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? (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 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: (a) \(2 \mathrm{meV}\) (b) \(\sqrt{\mathrm{meV}}\) (c) \(\sqrt{2 \mathrm{meV}}\) (d) \(\mathrm{meV}\)