Chapter 13

The ionization energy of He-atom in ground state may be (a) \(13.6 \mathrm{eV}\) (b) \(54.4 \mathrm{eV}\) (c) \(108.8 \mathrm{eV}\) (d) \(27.0 \mathrm{eV}\)

The binding energy for the third electron in the ground state of \(\mathrm{Li}\) -atom should be (a) \(108.8 \mathrm{eV}\) (b) \(122.4 \mathrm{eV}\) (c) \(30.6 \mathrm{eV}\) (d) \(27.2 \mathrm{eV}\)

Suppose that means were available for stripping 29 electrons from \({ }_{30} \mathrm{Zn}\) in vapours of this metal. The ionization energy for the last electron is (a) \(11.5 \mathrm{keV}\) (b) \(12.24 \mathrm{keV}\) (c) \(13.6 \mathrm{eV}\) (d) \(408 \mathrm{eV}\)

For an electron in a hydrogen atom, the wave function is given by \(\psi_{1 \mathrm{~s}}\) \(=(\pi / \sqrt{2}) e^{-r / a_{0}}\), where \(a_{0}\) is the radius of first Bohr's orbit and \(r\) is the distance from the nucleus with which probability of finding electron varies. What will be the ratio of probabilities of finding electrons at the nucleus to first Bohr's orbit \(a_{\mathrm{o}} ?\) (a) 0 (b) \(e\) (c) \(e^{2}\) (d) \(\frac{1}{e^{2}}\)

If \(n\) and \(l\) are, respectively, the principal and azimuthal quantum numbers, then the expression for calculating the total number of electrons in any energy level is (a) \(\sum_{l=1}^{l=n} 2(2 l+1)\) (b) \(\sum_{l=1}^{l=n-1} 2(2 l+1)\) (c) \(\sum_{l=0}^{l=n+1} 2(2 l+1)\) (d) \(\sum_{l=0}^{l=n-1} 2(2 l+1)\)

The charge on the electron and proton is reduced to half. Let the present value of the Rydberg constant is \(R\). What will be the new value of the Rydberg constant? (a) \(\frac{R}{2}\) (b) \(\frac{R}{4}\) (c) \(\frac{R}{8}\) (d) \(\frac{R}{16}\)

Which of the following element will have same number of electrons in s-as well as p-type of orbitals? (a) \(\mathrm{Fe}(Z=26)\) (b) \(\operatorname{Mg}(Z=12)\) (c) \(\operatorname{Ne}(Z=10)\) (d) \(\operatorname{Ar}(Z=18)\)

For the same electronic transition in the following atom or ion, the frequency of the emitted radiation will be maximum for (a) H-atom (b) D-atom (c) \(\mathrm{He}^{+}\) ion (d) \(\mathrm{Li}^{2+}\) ion

Number of electrons having \(m=0\) for sodium atom is (a) 2 (b) 5 (c) 7 (d) 3

An electron jumps from the fourth orbit to the first orbit in a H-atom. The number of photons liberated out will be (a) 1 (b) 2 (c) 3 (d) 6

The wavelength of radiation emitted out in the transition \(n=4\) to \(n=1\) in \(\mathrm{Li}^{2+}\) ion is (a) \(\frac{135 R}{16}\) (b) \(\frac{16}{135 R}\) (c) \(\frac{16 R}{135}\) (d) \(\frac{135}{16 R}\)

The average and the most probable distance from the nucleus for 1 s electron in hydrogen atom are, respectively \(\left(a_{\mathrm{o}}\right.\) is the first Bohr radius.), (a) \(a_{\mathrm{o}}, a_{\mathrm{o}}\) (b) \(a_{\mathrm{o}}, 1.5 a_{\mathrm{o}}\) (c) \(1.5 a_{0}, a_{\mathrm{o}}\) (d) \(1.5 a_{0}, 1.5 a_{\mathrm{o}}\)

The wavelength of a spectral line obtained by an electronic transition is inversely proportional to (a) Number of transit electrons (b) Nuclear charge of the atom (c) Energy difference of the related energy levels (d) Speed of the transit electron

The orbital angular momentum of an electron is \(\sqrt{3} \frac{h}{\pi}\). Which of the following may be the permissible value of angular momentum of this electron revolving in unknown Bohr orbit? (a) \(\frac{h}{\pi}\) (b) \(\frac{h}{2 \pi}\) (c) \(\frac{3 h}{2 \pi}\) (d) \(\frac{2 h}{\pi}\)

In H-atom, wave number ratio is \(108: 7\) is for (a) first Lyman and first Balmer transition (b) first Lyman and first Brackett transition (c) first Lyman and first Paschen transition (d) first Lyman and second Balmer transition

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition \(n=4\) to \(n=2\) of \(\mathrm{He}^{+}\) spectrum? (a) \(n=4\) to \(n=2\) (b) \(n=4\) to \(n=1\) (c) \(n=2\) to \(n=1\) (d) \(n=3\) to \(n=2\)

Number of possible spectral lines in the bracket series in hydrogen spectrum, when electrons present in the ninth excited state return to the ground state, is (a) 36 (b) 45 (c) 5 (d) 6

The mass of a particle is \(10^{-10} \mathrm{~g}\) and its diameter is \(10^{-4} \mathrm{~cm} .\) If its speed is \(10^{-6} \mathrm{~cm} / \mathrm{s}\) with \(0.0001 \%\) uncertainty in measurement, the minimum uncertainty in its position is (a) \(5.28 \times 10^{-8} \mathrm{~m}\) (b) \(5.28 \times 10^{-7} \mathrm{~m}\) (c) \(5.28 \times 10^{-6} \mathrm{~m}\) (d) \(5.28 \times 10^{-9} \mathrm{~m}\)

Uncertainty in the position of an electron (mass \(=9.1 \times 10^{-31} \mathrm{~kg}\) ) moving with a velocity \(300 \mathrm{~m} / \mathrm{s}\), accurate up to \(0.001 \%\), will be \(\left(h=6.3 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right)\) (a) \(5.76 \times 10^{-2} \mathrm{~m}\) (b) \(1.92 \times 10^{-2} \mathrm{~m}\) (c) \(3.84 \times 10^{-2} \mathrm{~m}\) (d) \(19.2 \times 10^{-2} \mathrm{~m}\)

The ratio of de-Broglie wavelength of electron and proton moving with the same speed is about (a) \(1836: 1\) (b) \(1: 1836\) (c) \(1: 1\) (d) \(1: 2\)

The circumference of the third orbit of \(\mathrm{He}^{+}\) ion is \(x \mathrm{~m} .\) The de-Broglie wavelength of electron revolving in this orbit will be (a) \(\frac{x}{3} \mathrm{~m}\) (b) \(3 x \mathrm{~m}\) (c) \(\frac{x}{9} \mathrm{~m}\) (d) \(9 x \mathrm{~m}\)

The momentum of a photon of wavelength \(6626 \mathrm{~nm}\) will be (a) \(10^{-28} \mathrm{~kg} \mathrm{~ms}^{-1}\) (b) \(10^{-25} \mathrm{~kg} \mathrm{~ms}^{-1}\) (c) \(10^{31} \mathrm{~kg} \mathrm{~m}^{-1}\) (d) zero

The energy of different orbitals in an atom or ion having only one electron, depends on (a) \(n\) only (b) \(n\) and \(l\) only (c) \(n, l\) and \(m\) only (d) \(n, l, m\) and \(s\)

The size of an orbital is given by (a) principal quantum number (b) azimuthal quantum number (c) magnetic quantum number (d) spin quantum number

The electron in the same orbital may be identified with the quantum number (a) \(n\) (b) \(l\) (c) \(m\) (d) s

The orbital angular momentum of an electron is 2 s orbital is (a) \(+\frac{1}{2} \cdot \frac{h}{2 \pi}\) (b) 0 (c) \(\frac{h}{2 \pi}\) (d) \(\sqrt{2} \frac{h}{2 \pi}\)

The orbital angular momentum of a 4p electron will be (a) 4. \(\frac{h}{2 \pi}\) (b) \(\sqrt{2} \cdot \frac{h}{2 \pi}\) (c) \(\sqrt{6} \cdot \frac{h}{4 \pi}\) (d) \(\sqrt{2} \cdot \frac{h}{4 \pi}\)

The quantum number which determines the shape of the orbital is (a) Magnetic quantum no. (b) Azimuthal quantum no. (c) Principal quantum no. (d) Spin quantum no.

Orbital with maximum symmetry is (a) p-orbital (b) s-orbital (c) \(d_{x y}\) -orbital (d) \(d_{z^{2}}\) -orbital

In presence of external magnetic field, p-orbital is (a) 3 -fold degenerate (b) 5 -fold degenerate (c) 7 -fold degenerate (d) non-degenerate

The number of orbitals of \(\mathrm{g}\) -type (a) 5 (b) 7 (c) 9 (d) 11

Which of the following orbital does not exist according to quantum theory? (a) \(5 \mathrm{~g}\) (b) \(4 \mathrm{f}\) (c) \(5 \mathrm{~h}\) (d) \(6 \mathrm{~h}\)

Number of orbitals represented by \(n=3\), \(l=2\) and \(m=+2\) is (a) 1 (b) 2 (c) 3 (d) 4

The number of nodal planes in \(2 \mathrm{p}_{\mathrm{x}}\) orbital is (a) zero (b) 1 (c) 2 (d) infinite

Which orbital is represented by the complete wave function, \(\psi_{410}\) ? (a) 4s (b) \(3 \mathrm{p}\) (c) \(4 \mathrm{p}\) (d) 4d

The number of radial nodes of \(3 \mathrm{~s}, 3 \mathrm{p}\) and \(3 \mathrm{~d}\) electrons are, respectively, (a) \(0,1,2\) (b) \(2,1,0\) (c) \(2,2,2\) (d) \(1,3,5\)

The process of successive addition of protons to the nucleus followed by an addition of the same number of electrons to the available orbitals in the sequence of increasing energy to obtain the electronic configuration of many electronic configuration of many electron atom, is known as (a) Pauli's exclusion principle (b) Hund's rule (c) Heisenberg's uncertainty principal (d) Aufbau principle

A completely filled \(d\) -orbital \(\left(\mathrm{d}^{10}\right)\) is of (a) Spherical symmetry (b) Octahedral symmetry (c) Tetrahedral symmetry (d) Unsymmetry

An atom have \(\mathrm{d}^{8}\) configuration. The maximum number of electrons in the same spin is (a) 5 (b) 3 (c) 8 (d) 2

The number of orbitals having \((n+l)\) \(<5\) is (a) 9 (b) 8 (c) 4 (d) 10

The total number of orbital for \((n+l)=4\) is (a) 4 (b) 16 (c) 32 (d) 9

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

If the numbers of orbitals of a particular type were \((3 l+1)\), but spin quantum numbers were only \(+1 / 2\) and \(-1 / 2\), then \(\mathrm{d}\) -type orbitals will contain a maximum of electrons. (a) 10 (b) 14 (c) 7 (d) 5

Which quantum number differs for the two electrons present in \(\mathrm{K}\) -shell of an atom? (a) Principal quantum number (b) Azimuthal quantum number (c) Magnetic quantum number (d) Spin quantum number

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

Correct set of quantum numbers defining the highest energy electron in scandium (I) ion is (a) \(n=3, l=1, m=0, s=-1 / 2\) (b) \(n=3, l=0, m=0, s=-1 / 2\) (c) \(n=4, l=0, m=0, s=+1 / 2\) (d) \(n=3, l=2, m=2, s=+1 / 2\)

How many unpaired electrons are present in ground state of chromium \((Z=24)\) ? (a) 1 (b) 5 (c) 6 (d) 0

\(\mathrm{K}\) and \(\mathrm{L}\) shell of an element are completely filled and there are 16 electrons in M-shell and 2 -electrons in N-shell. The atomic number of the element is (a) 18 (b) 28 (c) 22 (d) 26

The number of unpaired electron in G. S. first E.S. and second E.S. of \(\mathrm{S}(Z=16)\) are, respectively, (a) 0,2 and 4 (b) 2,4 and 6 (c) 0,4 and 6 (d) 2,4 and 4

The electronic structure of zinc \((Z=30)\) is \(2,8,18,2 .\) The electronic structure of gallium \((Z=31)\) will be (a) \(2,8,18,2,1\) (b) \(2,8,19,2\) (c) \(2,8,18,3\) (d) \(2,8,19,3\)