Chapter 4

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?

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?

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 \(l=1\) ?

An ion \(\mathrm{Mn}^{\mathrm{a}+}\) 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 \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\) ) \(\quad\) [2002] (a) \(2.1 \times 10^{-28}\) (b) \(2.1 \times 10^{-34}\) (c) \(0.5 \times 10^{-34}\) (d) \(5.0 \times 10^{-24}\)

Which of the following ions has the maximum magnetic moment? (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 \([\mathbf{2 0 0 3}]\) (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) \(10^{-25} \mathrm{~m}\)

The orbital angular momentum for an electron re volving in an orbit is given by \(\sqrt{\ell} /(l+1) \mathrm{h} / 2 \pi\). This momentum for an s electron will be given by \([\mathbf{2 0 0 3}]\) (a) \(+1 / 2 \cdot \mathrm{h} / 2 \pi\) (b) zero (c) \(\mathrm{h} / 2 \pi\) (d) \(\sqrt{2} \cdot \mathrm{h} / 2 \pi\)

The number of d electrons retained in \(\mathrm{Fe}^{2+}\) (At. number of \(\mathrm{Fe}=26\) ) ions is [2003] (a) 3 (b) 4 (c) 5 (d) 6

Which of the following sets of quantum numbers is correct for an electron in 4 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 \(\quad\) [2004] (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 \(=1.097 \times 10^{7}\) \(\mathrm{m}^{-1}\) ) \(\quad[\mathbf{2 0 0 4}]\) (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) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}, \mathrm{F}^{-}\) (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? (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 \(b\)

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) \(\mathrm{CN}^{-}, \mathrm{N}_{2}, \mathrm{C}_{2}{\underline{\phantom{xx}}}^{2}\) (c) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}, \mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}, \mathrm{NO}_{3}-\) (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) \(10 \mathrm{~h} / \pi\) (d) \(2.5 \mathrm{~h} / \pi\)

Which one of the following sets of ions represents a collection of isoelectronic species? [2006] (a) \(\mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{Ca}^{2+}, \mathrm{Sc}^{3+}\) (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? (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, \(\mathrm{em}=9.1 \times\) \(\left.10^{-31} \mathrm{~kg}\right): \quad[\mathbf{2 0 0 9}]\) (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) \(2.5 \mathrm{~nm}\)

The energy required to break one mole of \(\mathrm{C} 1-\mathrm{Cl}\) bonds in \(\mathrm{C}_{12}\) is \(242 \mathrm{~kJ} \mathrm{~mol}^{-1}\). the longest wavelength of light capable of breaking a single \(\mathrm{Cl}-\mathrm{C} 1\) bond is \(\left(\mathrm{c}=3 \times 10^{\mathrm{s}} \mathrm{ms}^{-1}\right.\) and \(\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1} \quad\) [2010] (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 \(l\) \([2012]\) (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 \(\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)\) (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: \([\mathbf{2 0 1 4}]\) (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: [2016] (a) \(2 \mathrm{meV}\) (b) \(\sqrt{\mathrm{meV}}\) (c) \(\sqrt{2 \mathrm{meV}}\) (d) \(\mathrm{meV}\)