Chapter 4

The correct order of number of unpaired electrons in the ion \(\mathrm{Cu}^{2+} \mathrm{Ni}^{2+}, \mathrm{Fe}^{3+}\) and \(\mathrm{Cr}^{3+}\) is (a) \(\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}>\mathrm{Cr}^{3+}>\mathrm{Fe}^{3+}\) (b) \(\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}>\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}\) (c) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}\) (d) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}\)

The magnetic moment of \(\mathrm{Cu}^{2+}\) ion is (a) \(2.6\) (b) \(2.76\) (c) \(1.73\) (d) 0

Given: the mass of electron is \(9.11 \times 10^{-31} \mathrm{~kg}\) Planck constant is \(6.626 \times 10^{-34} \mathrm{Js}\), the uncertainty involved in the measurement of velocity within a distance of \(0.1 \AA\) is (a) \(5.79 \times 10^{8} \mathrm{~ms}^{-1}\) (b) \(5.79 \times 10^{5} \mathrm{~ms}^{-1}\) (c) \(5.79 \times 10^{6} \mathrm{~ms}^{-1}\) (d) \(5.79 \times 10^{7} \mathrm{~ms}^{-1}\)

The energy ratio of a photon of wavelength \(3000 \AA\) and \(6000 \AA\) is (a) \(1: 1\) (b) \(2: 1\) (c) \(1: 2\) (d) \(1: 4\)

The energy of second Bohr orbit of the hydrogen atom is \(-328 \mathrm{~kJ} \mathrm{~mol}^{-1}\), hence the energy of fourth bohr orbit would be (a) \(-164 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-41 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-82 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-1312 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

The de Broglie wavelength associated with a particle of mass \(10^{-6} \mathrm{~kg}\) moving with a velocity of \(10 \mathrm{~ms}^{-1}\) is (a) \(6.63 \times 10^{-7} \mathrm{~m}\) (b) \(6.63 \times 10^{-16} \mathrm{~m}\) (c) \(6.63 \times 10^{-21} \mathrm{~m}\) (d) \(6.63 \times 10^{-29} \mathrm{~m}\)

In hydrogen atom, energy of first excited state is \(-3.4\) \(\mathrm{eV}\). The kinetic energy of the same orbit of hydrogen atom would be (a) \(+3.4 \mathrm{eV}\) (b) \(+6.8 \mathrm{eV}\) (c) \(-13.6 \mathrm{eV}\) (d) \(+13.6 \mathrm{eV}\)

Electron energy of a photon is given as: \(\Delta \mathrm{E} /\) atom \(=3.03 \times 10^{-19} \mathrm{~J}\) atom \(^{-1}\) then, the wavelength of the photon is (a) \(6.56 \mathrm{~nm}\) (b) \(65.6 \mathrm{~nm}\) (c) \(656 \mathrm{~nm}\) (d) \(0.656 \mathrm{~nm}\) Given, \(\mathrm{h}\) (Planck constant) \(=6.63 \times 10^{-34} \mathrm{Js} \mathrm{c}\) (velocity of light \()=3.00 \times 10^{8} \mathrm{~ms}^{-1}\)

If the nitrogen atom has electronic configuration \(1 \mathrm{~s}^{7}\), it would have energy lower than that of the normal ground state configuration \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{3}\), because the electrons would be closer to the nucleus. Yet \(1 \mathrm{~s}^{7}\) is not observed because it violates (a) Heisenberg uncertainty principle (b) Hund's rule (c) Pauli's exclusion principle (d) Bohr postulates of stationary orbits

Radial nodes present in \(3 \mathrm{~s}\) and \(2 \mathrm{p}\) orbitals are respectively (a) 0,2 (b) 2,0 (c) 2,1 (d) 1,2

The radius of which of the following orbits is same as that of the first Bohr's orbit of hydrogen atom? (a) \(\mathrm{He}^{+}(\mathrm{n}=2)\) (b) \(\mathrm{Li}^{2+}(\mathrm{n}=2)\) (c) \(\mathrm{Li}^{2+}(\mathrm{n}=3)\) (d) \(\mathrm{Be}^{3+}(\mathrm{n}=2)\)

The wavelength associated with a golf ball weighing \(200 \mathrm{~g}\) and moving at a speed of \(5 \mathrm{~m} / \mathrm{h}\) is of the order (a) \(10^{-10} \mathrm{~m}\) (b) \(10^{-20} \mathrm{~m}\) (c) \(10^{-30} \mathrm{~m}\) (d) \(10^{-40} \mathrm{~m}\)

Which of the following statement(s) are correct? (1) the electronic configuration of \(\mathrm{Cr}\) is \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (atomic number of \(\mathrm{Cr}=24\) ) (2) the magnetic quantum number may have a negative value (3) in silver atom, 23 electrons have a spin of one type and 24 of the opposite type (atomic number of \(\mathrm{Ag}=47\) ) (4) the oxidation state of nitrogen in \(\mathrm{HN}\), is \(-3\) (a) \(1,2,3\) (b) \(2,3,4\) (c) 3,4 (d) \(1,2,4\)

For a d-electron, the orbital angular momentum is (a) \(\sqrt{6 h}\) (b) \(\sqrt{2 h}\) (c) \(\mathrm{h}\) (d) \(2 \mathrm{~h}\)

The orbital angular momentum of an electron in \(2 \mathrm{~s}\) orbital is (a) \(+\frac{1}{2} \cdot \frac{\mathrm{h}}{2 \pi}\) (b) zero (c) \(\frac{h}{2 \pi}\) (d) \(\sqrt{2} \frac{h}{2 \pi}\)

The mass of an electron is \(\mathrm{m}\). Its charge is \(\mathrm{e}\) and it is accelerated from rest through a potential difference \(\mathrm{V}\). The velocity acquired by the electron will be (a) \(\sqrt{\mathrm{V} / \mathrm{m}}\) (b) \(\sqrt{\mathrm{eV} / \mathrm{m}}\) (c) \(\sqrt{2 \mathrm{e}} \mathrm{V} / \mathrm{m}\) (d) none

An atom A has the electronic configuration of \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2}\) \(2 \mathrm{p}^{1}\). Atom B has the electronic configuration of \(1 \mathrm{~s}^{2}\) \(2 \mathrm{~s}^{2} 2 \mathrm{p}^{1} .\) The empirical formula of the compound obtained from the reaction of \(\mathrm{A}\) and \(\mathrm{B}\) is (a) \(\mathrm{AB}\) (b) \(\mathrm{AB}_{3}\) (c) \(\mathrm{A}_{3} \mathrm{~B}_{3}\) (d) \(\mathrm{A}, \mathrm{B}_{6}\)

The shortest wavelength in hydrogen spectrum of Lyman series when \(\mathrm{R}_{H}=109678 \mathrm{~cm}^{-1}\) is (a) \(1002.7 \AA\) (b) \(1215.67 \AA\) (c) \(1127.30 \AA\) (d) \(911.7 \AA\)

Correct set of four quantum numbers for the valence (outermost) electron of rubidium \((\mathrm{Z}=37)\) is (a) \(5,0,0, \pm 1 / 2\) (b) \(6,0,0,+1 / 2\) (c) \(5,1,1, \pm 1 / 2\) (d) \(5,1,0, \pm 1 / 2\)

The ionization energy of hydrogen atom is \(13.6 \mathrm{eV}\). What will be the ionization energy of \(\mathrm{He}^{+}\)? (a) \(13.6 \mathrm{eV}\) (b) \(54.4 \mathrm{eV}\) (c) \(122.4 \mathrm{eV}\) (d) zero

Predict the total spin in \(\mathrm{Ni}^{2+}\) ion (a) \(\pm 5 / 2\) (b) \(\pm 3 / 2\) (c) \(\pm 1 / 2\) (d) \(\pm 1\)

For the electronic transition from \(\mathrm{n}=2 \rightarrow \mathrm{n}=1\), which of the following will produce shortest wave length? (a) \(\mathrm{Li}^{2+}\) ion (b) D atom (c) \(\mathrm{He}^{+}\)ion (d) \(\mathrm{H}\) atom

Probability of finding the electron \(\psi^{2}\) of \(\mathrm{s}\) orbital doesn't depend upon (a) azimuthal quantum number. (b) energy of s orbital (c) principal quantum number (d) distance from nucleus (r)

The charge cloud of a single electron in a \(2 \mathrm{p}_{\mathrm{x}}\) atomic orbital has two lobes of electron density. This means (a) there is a high probability of locating the electron in a \(2 \mathrm{p}_{\mathrm{x}}\) atomic orbital at values of \(\mathrm{x}>0\) (b) there is a great probability of finding a p electron right at the nucleus (c) there is a high probability of locating it values of \(\mathrm{x}<0\) but no probability at alloy locating if any where in the \(y z\) plane along which \(x=0\). (d) both (a) and (c)

The de Broglie wavelength associated with a ball of mass \(1 \mathrm{~kg}\) having a kinetic energy \(0.5 \mathrm{~J}\) is (a) \(6.626 \times 10^{-34} \mathrm{~m}\) (b) \(13.2 \times 10^{-34} \mathrm{~m}\) (c) \(10.38 \times 10^{-21} \mathrm{~m}\) (d) \(6.626 \AA\)

The size of a microscopic particle is one micron and its mass is \(6 \times 10^{-13} \mathrm{gm} .\) If its position may be measured to within \(0.1 \%\) of its size, the uncertainty in velocity, in \(\mathrm{cm} \mathrm{s}^{-1}\), is approximately (a) \(10^{-6} / 3 \pi\) (b) \(10^{-7} / 2 \pi\) (c) \(10^{-5} / 4 \pi\) (d) \(10^{-7} / 4 \pi\)

The electrons, identified by quantum numbers \(\mathrm{n}\) and \(l\) (i) \(\mathrm{n}=4 . l=1\) (ii) \(\mathrm{n}=4, l=0\) (iii) \(\mathrm{n}=3, l=2\) (iv) \(\mathrm{n}\) \(=3, l=1\) can be placed in order of increasing energy from the lowest to highest as (a) (iv) \(<(i i)<(i i i)<(i)\) (b) (ii) \(<(\mathrm{iv})<(\mathrm{i})<(\mathrm{iii})\) (c) (i) \(<(\mathrm{iii})<(\mathrm{ii})<\) (iv) (d) (iii) < (i) < (iv) < (ii)

What is the wavelength of the radiation emitted produced in a line in the Lyman series when an electron falls from fourth stationary state in hydrogen atom? \(\left(\mathrm{R}_{\mathrm{H}}=1.1 \times 10^{7} \mathrm{~m}^{-1}\right)\) (a) \(96.97 \mathrm{~nm}\) (b) \(969.7 \mathrm{~nm}\) (c) \(9.697 \mathrm{~nm}\) (d) none

Rearrange the following (I to IV) in the order of in creasing masses and choose the correct answer from (a), (b), (c), (d). (atomic masses: \(\mathrm{N}=14, \mathrm{O}=\) \(16, \mathrm{Cu}=63)\) I. 1 molecule of oxygen II. 1 atom of nitrogen III. \(1 \times 10^{10} \mathrm{~g}\) molecular weight of oxygen IV. \(1 \times 10^{-18} \mathrm{~g}\) atomic weight of copper (a) \(\mathrm{II}<\mathrm{I}<\mathrm{IV}<\mathrm{III}\) (b) \(\mathrm{IV}<\mathrm{III}<\mathrm{II}<\mathrm{I}\) (c) \(\mathrm{II}<\mathrm{III}<\mathrm{I}<\mathrm{IV}\) (d) \(\mathrm{III}<\mathrm{IV}<\mathrm{I}<\mathrm{II}\)

An electron in a hydrogen atom in its ground state absorbs \(1: 50\) times as much energy as the minimum required for it to escape from the atom. What is the wavelength of the emitted electron? (a) \(4.7 \mathrm{~A}\) (b) \(4.70 \mathrm{pm}\) (c) \(6.3 \mathrm{~A}\) (d) \(8.4 \AA\)

In hydrogen atom, an orbit has a diameter of about \(16.92 \mathrm{~A}\). What is the maximum number of electrons that can be accommodated? (a) 32 (b) 16 (c) 48 (d) 72

A 1000 watt radio transmitter operates at a frequen cy of \(880 \mathrm{kc} / \mathrm{sec}\). How many photons per sec does it emit? \(\left[\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right]\) (a) \(2.51 \times 10^{10}\) (b) \(2.27 \times 10^{2 n}\) (c) \(1.72 \times 10^{10}\) (d) \(1.77 \times 10^{27}\)

How many moles of electrons weigh one kilogram? (mass of electron \(=9.108 \times 10^{-31} \mathrm{~kg}\), Avogadro number \(\left.=6.023 \times 10^{23}\right)\) (a) \(6.023 \times 10^{23}\) (b) \(1 / 9.108 \times 10^{31}\) (c) \(\frac{6.023}{9.108} \times 10^{34}\) (d) \(\frac{1}{9.108 \times 6.023} \times 10^{2}\)

Calculate the wavelength and energy of the radiation emitted for the electronic transition from infinity \((\infty)\) to stationary state first of the hydrogen atom. \(\left(\mathrm{R}_{\mathrm{u}}=1.09678 \times 10^{7} \mathrm{~m}^{-1}, \mathrm{~h}=6.6256 \times 10^{-14} \mathrm{Js}\right)\) (a) \(2.18 \times 10^{-21} \mathrm{~kJ}\) (b) \(3.18 \times 10^{-22} \mathrm{~kJ}\) (c) \(1.18 \times 10^{-23} \mathrm{~kJ}\) (d) \(2.18 \times 10^{-31} \mathrm{~kJ}\)

Some of the following sets of quantum numbers are correct for a \(4 \mathrm{~d}\) electron. Which are correct sets? (a) \(4,3,2,+\frac{1}{2}\) (b) \(4,2,1,0\) (c) \(4,2,-2,+\frac{1}{2}\) (d) \(4,2,1,-\frac{1}{2}\)

Which of the following statement (s) is /are incorrect ? (a) 3 s orbital has 2 radical nodes. (b) Electronic configuration of \(\mathrm{Co}^{3+}\) is \(4 \mathrm{~s}^{2} 3 \mathrm{~d}^{4}\). (c) \(2 \mathrm{p}\) orbital has 1 radial node. (d) Node is a region around the nucleus of an atom where probability of finding electron is maximum.

Which of the following factors induce larger angle of deflection in Rutherford's scattering experiment? (a) The initial kinetic energy of striking \(\alpha\)-particles must be large (b) The initial kinetic energy of striking \(\alpha\)-particles must be small (c) The nucleus to which the \(\alpha\)-particles are striking must have small atomic number (d) The nucleus to which the \(\alpha\)-particles are striking must have high atomic number

In which of the orbital/orbitals radial node and angular nodes are same? (a) \(3 \mathrm{p}\) (b) \(4 \mathrm{p}\) (c) \(6 \mathrm{f}\) (d) \(5 \mathrm{~d}\)

Four different set of quantum numbers for 4 electrons are given below: \(\mathrm{e}_{1}=4,0,0-1 / 2 ; \mathrm{c}_{2}=3,1,1-1 / 2\) \(\mathrm{e}_{3}=3,2,2+1 / 2 ; \mathrm{e}_{4}=3,0,0,+1 / 2\) Then which of the following order of energies of \(\mathrm{e}_{1}, \mathrm{e}_{2}\) \(e_{3}\) and \(e_{4}\) are against the quantum rules ? (a) \(\mathrm{e}_{1}>\mathrm{e}_{2}>\mathrm{e}_{1}>\mathrm{e}_{4}\) (b) \(e_{4}>\mathrm{e}_{3}>\mathrm{e}_{2}>\mathrm{e}_{1}\) (c) \(\mathrm{e}_{3}>\mathrm{e}_{1}>\mathrm{e}_{2}>\mathrm{e}_{4}\) (d) \(e_{2}>e_{3}>c_{4}>c_{1}\)

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 \(n=4, l=1, m=2, s=+1 / 2\) (c) Angular momentum of 3 s electron is one. (d) \((\mathrm{n}+I)\) 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 \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (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

According to de Broglie concept, all material particles posses wave character as well as particle character. The wave associated with a moving particle is called matter wave. The wavelength of the matter wave is given by the equation \(\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}\) where \(\mathrm{p}\) is the momentum of the particle, " \(\mathrm{m}\) ' is the mass of the particle and ' \(\mathrm{v}^{\prime}\) is the velocity of the particle. ' \(\mathrm{h}\) ' is called Planck's constant. The wavelength associated with an electron (mass = \(9.11 \times 10^{-11} \mathrm{~kg}\) ) moving with a velocity of \(10^{5} \mathrm{~m} \mathrm{~s}^{-1}\) 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) \(7.27 \mathrm{~m}\)

According to de Broglie concept, all material particles posses wave character as well as particle character. The wave associated with a moving particle is called matter wave. The wavelength of the matter wave is given by the equation \(\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}\) where \(\mathrm{p}\) is the momentum of the particle, " \(\mathrm{m}\) ' is the mass of the particle and ' \(\mathrm{v}^{\prime}\) is the velocity of the particle. ' \(\mathrm{h}\) ' is called Planck's constant. The de Broglie wave length of a moving particle of mass \(1 \mathrm{~g}\) is \(6.625 \times 10^{-3} \mathrm{~m}\). The velocity of the particle is (a) \(100 \mathrm{~cm} \mathrm{~s}^{-1}\) (b) \(100 \mathrm{~m} \mathrm{~s}^{-1}\) (c) \(10 \mathrm{~ms}^{-1}\) (d) \(1000 \mathrm{~m} \mathrm{~s}^{-1}\)

According to de Broglie concept, all material particles posses wave character as well as particle character. The wave associated with a moving particle is called matter wave. The wavelength of the matter wave is given by the equation \(\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}\) where \(\mathrm{p}\) is the momentum of the particle, " \(\mathrm{m}\) ' is the mass of the particle and ' \(\mathrm{v}^{\prime}\) is the velocity of the particle. ' \(\mathrm{h}\) ' is called Planck's constant. Particle A moving with a certain velocity has de Broglie wavelength of \(1 \mathrm{~A}\). If the particle B has mass \(20 \%\) and velocity \(80 \%\) of that of \(A\), the de Broglie wavelength of B will be (a) \(1.6 \AA\) (b) \(16 \AA\) (c) \(4.0 \AA\) (d) \(6.25 \AA\)

The substances which contain atoms with unpaired electrons in their orbitals behave as paramagnetic substances. Such substances are weakly attracted by the magnetic field. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment is related to the number of unpaired electrons according to the following relation. Magnetic moment, \(\mu=\sqrt{n(n+2)} B M\) Where, \(\mathrm{n}\) - number of unpaired electrons. BM stands for Bohr Magneton, a unit of magnetic moment. Which of the following ions has magnetic momen equal to that of \(\mathrm{Ti}^{3+}\) (a) \(\mathrm{Ni}^{2+}\) (b) \(\mathrm{Co}^{2+}\) (c) \(\mathrm{Fe}^{2+}\) (d) \(\mathrm{Cu}^{2+}\)

The substances which contain atoms with unpaired electrons in their orbitals behave as paramagnetic substances. Such substances are weakly attracted by the magnetic field. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment is related to the number of unpaired electrons according to the following relation. Magnetic moment, \(\mu=\sqrt{n(n+2)} B M\) Where, \(\mathrm{n}\) - number of unpaired electrons. BM stands for Bohr Magneton, a unit of magnetic moment. 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 \(\begin{array}{cccc}\mathrm{n} & l & \mathrm{~m} & \mathrm{~s} \\ 2 & 0 & 0 & +1 / 2 \\ 2 & 0 & 0 & -1 / 2\end{array}\) (c) (d) Principal quantum no. \(n\) 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) \([\mathrm{Ar}] 3 \mathrm{~d}^{\mathrm{s}} 4 \mathrm{~s}^{2}\) (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) \(\mathrm{T}_{1}^{+3}\) (s) \(\mathrm{Cu}^{+}\) (t) Ni