Chapter 4

The frequency of radiation emitted when the electron falls from \(\mathrm{n}=4\) to \(\mathrm{n}=1\) in a hydrogen atom will be (Given ionization energy of \(\mathrm{H}=2.18 \times 10^{18} \mathrm{~J}\) atom \(^{-1}\) and \(\left.\mathrm{h}=6.625 \times 10^{-34} \mathrm{Js}\right)\) (a) \(1.54 \times 10^{15} \mathrm{~s}^{-1}\) (b) \(1.03 \times 10^{15} \mathrm{~s}^{-1}\) (c) \(3.08 \times 10^{15} \mathrm{~s}^{-1}\) (d) \(2.00 \times 10^{15} \mathrm{~s}^{-1}\)

Among the following series of transition metal ions, the one where all metal ion have \(3 \mathrm{~d}^{2}\) electronic configuration is (a) \(\mathrm{Ti}^{3+}, \mathrm{V}^{2+}, \mathrm{Cr}^{3+}, \mathrm{Mn}^{4+}\) (b) \(\mathrm{Ti}^{+}, \mathrm{V}^{4+}, \mathrm{Cr}^{6+}, \mathrm{Mn}^{7+}\) (c) \(\mathrm{Ti}^{4+}, \mathrm{V}^{3+}, \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+}\) (d) \(\mathrm{Ti}^{2+}, \mathrm{V}^{3+}, \mathrm{Cr}^{4+}, \mathrm{Mn}^{5+}\) (At. wt \(\mathrm{Ti}=22, \mathrm{~V}=23, \mathrm{Cr}=24, \mathrm{Mn}=25\) )

The relationship between energy \(\mathrm{E}\), of the radiation with a wavelength \(8000 \AA\) and the energy of the ra diation with a wavelength \(16000 \AA\) is (a) \(\mathrm{E}_{1}=2 \mathrm{E}_{2}\) (b) \(\mathrm{E}_{1}=4 \mathrm{E}_{2}\) (c) \(\mathrm{E}_{1}=6 \mathrm{E}_{2}\) (d) \(E_{1}=E_{2}\)

An electron is moving in Bohr's fourth orbit, its de-Broglie wavelength is \(X\). What is the circumference of the fourth orbit? (a) \(2 \lambda\) (b) \(2 / \lambda\) (c) \(3 \lambda\) (d) \(4 \lambda\)

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) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}\)

Find the magnetic moment of a divalent ion in aqueous solution if its atomic number is 25 . (a) \(6.9 \mathrm{~B} . \mathrm{M}\) (b) \(5.9 \mathrm{~B} . \mathrm{M}\) (c) \(4.9 \mathrm{~B} . \mathrm{M} .\) (d) \(3.0 \mathrm{~B} . \mathrm{M}\)

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) \(+13.6 \mathrm{eV}\)

The velocity of an electron in the second shell of hydrogen atom is (a) \(10.94 \times 10^{\circ} \mathrm{ms}^{-1}\) (b) \(18.88 \times 10^{6} \mathrm{~ms}^{-1}\) (c) \(1.888 \times 10^{6} \mathrm{~ms}^{-1}\) (d) \(1.094 \times 10^{6} \mathrm{~ms}^{-1}\)

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, 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) \(\operatorname{Li}^{2+}(\mathrm{n}=3)\) (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 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) \(\sqrt{2} \mathrm{~h}\) (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) \(\frac{\mathrm{h}}{2 \pi}\) (d) \(\sqrt{2} \frac{\mathrm{h}}{2 \pi}\)

The mass of an electron is \(\mathrm{m}\). Its charge is 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

A \(600 \mathrm{~W}\) mercury lamp emits monochromatic radiation of wavelength \(331.3 \mathrm{~nm}\). How many photons are emitted from the lamp per second? \(\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s} ;\right.\) velocity of light \(=3 \times 10^{8} \mathrm{~ms}^{-1}\) (a) \(1 \times 10^{19}\) (b) \(1 \times 10^{20}\) (c) \(1 \times 10^{21}\) (d) \(1 \times 10^{23}\)

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 increasing order (lowest first) for the values of \(\mathrm{e} / \mathrm{m}\) (charge/mass) for electron (e), proton (p), neutron (n) and alpha particle (a) is (a) \(\mathrm{n}, \mathrm{p}, \mathrm{a}, \mathrm{e}\) (b) \(\mathrm{n}, \mathrm{p}, \mathrm{e}, \mathrm{a}\) (c) \(\mathrm{n}, \mathrm{a}, \mathrm{p}, \mathrm{e}\) (d) \(\mathrm{e}, \mathrm{p}, \mathrm{n}, \mathrm{a}\)

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

If \(S\), be the specific charge \((\mathrm{e} / \mathrm{m})\) of cathode rays and \(\mathrm{S}_{2}\) be that of positive rays then which is true? (a) \(\mathrm{S}_{1}=\mathrm{S}_{2}\) (b) \(\mathrm{S}_{1}<\mathrm{S}_{2}\) (c) \(\mathrm{S}_{1}>\mathrm{S}_{2}\) (d) None of these

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

For \(\mathrm{n}=2\) the correct set of \(\ell, \mathrm{m}\) are (a) \(\ell=2, \mathrm{~m}=-2,-1,0+1,+2\) (b) \(\ell=1 \mathrm{~m}=-2,-1,0+1,+2\) (c) \(\ell=1 \mathrm{~m}=-1,0,+1\) (d) \(\ell=0 \mathrm{~m}=-1,0,+1\)

Probability of finding the electron \(\psi^{2}\) of 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 \(x<0\) but no probability at alloy locating if any where in the yz plane along which \(x=0\). (d) both (a) and (c)

The wavelength of the de Broglie wave of the electron revolving in the fifth orbit of the hydrogen atom is \(\left(\mathrm{r}_{0}\right.\) is the Bohr's radius \(=0.529 \mathrm{~A}\) ) (a) \(20 \mathrm{r}_{0}\) (b) \((10 \pi) \mathrm{r}_{0}\) (c) \(5 \pi \mathrm{r}_{0}\) (d) \(15 \pi \mathrm{r}_{\mathrm{d}}\)

A monoenergetic electron beam with a de Broglie wavelength of \(x \AA\) is accelerated till its wavelength is halved. By what factor is its kinetic energy changed? (a) 8 (b) 6 (c) 4 (d) 3

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) \(<\) (iii) \(<(i i)<\) (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) II \(<\mathrm{I}<\mathrm{IV}<\mathrm{III}\) (b) IV < III < II < I (c) II \(<\mathrm{III}<\mathrm{I}<\mathrm{IV}\) (d) III \(<\) IV \(<\mathrm{I}<\mathrm{II}\)

If the shortest wavelength of \(\mathrm{H}\) atom in Lyman series is 'a', then longest wavelength in Balmer series of \(\mathrm{He}^{+}\)is (a) \(\mathrm{a} / 4\) (b) \(5 \mathrm{a} / 9\) (c) \(4 \mathrm{a} / 9\) (d) \(9 \mathrm{a} / 5\)

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) \(2.51 \times 10^{30}\) (b) \(2.27 \times 10^{28}\) (c) \(1.72 \times 10^{30}\) (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) \(\frac{6.023}{9.108} \times 10^{54}\) (d) \(\frac{1}{9.108 \times 6.023} \times 10^{8}\)

Calculate the wavelength and energy of the radiation emitted for the electronic transition from infinity \((\infty)\) to stationary state first of the hydrogen atom. \(\left(\mathrm{R}_{\mathrm{H}}=1.09678 \times 10^{7} \mathrm{~m}^{-1}, \mathrm{~h}=6.6256 \times 10^{-34} \mathrm{Js}\right)\) (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) \(4,2,1,-\frac{1}{2}\)

\(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}(\mathrm{Cr}=24)\) has a magnetic moment of \(3.83\) B.M. The incorrect distribution of 3 d electrons in the chromium of the complex is (a) \(3 \mathrm{~d}_{x y}^{1} 3 \mathrm{~d}_{y z}^{1} 3 \mathrm{~d}^{1}\) (b) \(3 \mathrm{~d}_{x y}^{1} 3 \mathrm{~d}_{y z}^{1} 3 \mathrm{~d}^{1} z^{2}\) (c) \(3 \mathrm{~d}^{1} 2 \mathrm{~d}^{1} x^{2}-y^{2} 3 \mathrm{~d}^{1} z^{2} 3 \mathrm{~d}^{1}{\underline{\phantom{xx}}}_{x z}\) (d) \(3 \mathrm{~d}_{x y}^{1} 3 \mathrm{~d}^{1} x^{2}-y^{2} 3 d_{y z}^{1}\)

Which of the following statement (s) is /are incorrect? (a) \(3 \mathrm{~s}\) 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

Energy of level \(1,2,3\) of a certain atom corresponds to increasing value of energy \(\mathrm{E}_{1}<\mathrm{E}_{2}<\mathrm{E}_{3}\). If \(\lambda_{1}, \lambda_{2}\) and \(\lambda\) are the wavelength of radiation corresponding to transition \(3 \rightarrow 2,2 \rightarrow 1\) and \(3 \rightarrow 1\) respectively. Which of following statement is/are correct? (a) \(\frac{1}{\lambda_{2}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{3}}\). (b) \(\lambda_{2}=\frac{\lambda_{1} \lambda_{3}}{\lambda_{1}+\lambda_{2}}\). (c) \(\frac{1}{\lambda_{3}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}\). (d) \(\lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}\).

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