Chapter 2

The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{Li}^{2+}\) is \(\Delta \mathrm{R}_{1}\). The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{He}^{+}\)is \(\Delta \mathrm{R}_{2}\). Ratio \(\Delta \mathrm{R}_{1}: \Delta \mathrm{R}_{2}\) is (a) \(8: 3\) (b) \(3: 8\) (c) \(2: 3\) (d) \(3: 2\)

In the sixth period, the orbitals that are filled are: [Main Sep. \(\mathbf{0 5}, \mathbf{2 0 2 0}\) (I)] (a) \(6 s, 4 f, 5 d, 6 p\) (b) \(6 s, 5 d, 5 f, 6 p\) (c) \(6 s, 5 f, 6 d, 6 p\) (d) \(6 s, 6 p, 6 d, 6 f\)

The region in the electromagnetic spectrum where the Balmer series lines appear is: (a) Visible (b) Microwave (c) Infrared (d) Ultraviolet

The de Broglie wavelength of an electron in the \(4^{\text {th }}\) Bohr orbit is: [Main Jan. 09, 2020 (I)] (a) \(2 \pi \mathrm{a}_{0}\) (b) \(4 \pi \mathrm{a}_{0}\) (c) \(6 \pi \mathrm{a}_{0}\) (d) \(8 \pi \mathrm{a}_{0}\)

The correct statement about probability density (except at infinite distance from nucleus) is: [Main Sep. \(\mathbf{0 5}, \mathbf{2 0 2 0}\) (II)] (a) It can be zero for \(1 s\) orbital (b) It can be negative for \(2 p\) orbital (c) It can be zero for \(3 p\) orbital (d) It can never be zero for \(2 s\) orbital

The shortest wavelength of \(\mathrm{H}\) atom in the Lyman series is \(\lambda_{1}\). The longest wavelength in the Balmer series is \(\mathrm{He}^{+}\)is : (a) \(\frac{36 \lambda_{1}}{5}\) (b) \(\frac{5 \lambda_{1}}{9}\) (c) \(\frac{9 \lambda_{1}}{5}\) (d) \(\frac{27 \lambda_{1}}{5}\)

If \(p\) is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength \(\lambda\), then for \(1.5 p\) momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function): [Main April 8, 2019 (II)] (a) \(\frac{3}{4} \lambda\) (b) \(\frac{1}{2} \lambda\) (c) \(\frac{2}{3} \lambda\) (d) \(\frac{4}{9} \lambda\)

Consider the hypothetical situation where the azimuthal quantum number, \(l\), takes values \(0,1,2, \ldots . n+1\), where \(n\) is the principal quantum number. Then, the element with atomic number : [Main Sep. 03, 2020 (II)] (a) 9 is the first alkali metal (b) 13 has a half-filled valence subshell (c) 8 is the first noble gas (d) 6 has a \(2 p\)-valence subshell

For the Balmer series in the spectrum of \(\mathrm{H}\) atom, \(\bar{v}=R_{H}\left\\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\\}\), the correct statements among (I) to (IV) are: (I) As wavelength decreases, the lines in the series converge (II) The integer \(n_{1}\) is equal to 2 (III)The lines of longest wavelength corresponds to \(n_{2}=3\) (IV) The ionization energy of hydrogen can be calculated from wave number of these lines (a) (I), (III), (IV) (b) (I), (II), (III) (c) (I), (II), (IV) (d) (II), (III), (IV)

If the de Broglie wavelength of the electron in \(\mathrm{n}^{\text {th }}\) Bohr orbit in a hydrogenic atom is equal to \(1.5 \pi \mathrm{a}_{0}\left(\mathrm{a}_{0}\right.\) is Bohr radius), then the value of \(\mathrm{n} / \mathrm{z}\) is : \(\quad\) [Main Jan. \(12,2019(\mathrm{II})]\) (a) \(0.40\) (b) \(1.50\) (c) \(1.0\) (d) \(0.75\)

The radius of the second Bohr orbit, in terms of the Bohr radius, \(a_{0}\), in \(\mathrm{Li}^{2+}\) is: (a) \(\frac{2 a_{0}}{3}\) (b) \(\frac{4 a_{0}}{9}\) (c) \(\frac{4 a_{0}}{3}\) (d) \(\frac{2 a_{0}}{9}\)

The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is: [Main Online April 15, 2018 (II)] (a) \(4 \times 0.529 \AA\) (b) \(2 \pi \times 0.529 \AA\) (c) \(\frac{0.529}{2 \pi} \AA\) (d) \(0.529 \AA\)

Among the following, the energy of \(2 s\) orbital is lowest in: (a) \(\mathrm{K}\) (b) \(\mathrm{H}\) (c) Li (d) \(\mathrm{Na}\)

At temperature \(\mathrm{T}\), the average kinetic energy of any particle is \(\frac{3}{2} \mathrm{kT}\). The de Broglie wavelength follows the order : [Main Online April 11, 2015] (a) Visible photon > Thermal neutron > Thermal electron (b) Thermal proton \(>\) Thermal electron \(>\) Visible photon (c) Thermal proton \(>\) Visible photon \(>\) Thermal electron (d) Visible photon \(>\) Thermal electron \(>\) Thermal neutron

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are : (a) Lyman and Paschen (b) Balmer and Brackett (c) Brackett and Pfund (d) Paschen and Pfund

The de-Broglie wavelength of a particle of mass \(6.63 \mathrm{~g}\) moving with a velocity of \(100 \mathrm{~ms}^{-1}\) is: [Main Online April 12, 2014] (a) \(10^{-33} \mathrm{~m}\) (b) \(10^{-35} \mathrm{~m}\) (c) \(10^{-31} \mathrm{~m}\) (d) \(10^{-25} \mathrm{~m}\)

For any given series of spectral lines of atomic hydrogen, let \(\Delta \bar{v}=\bar{v}_{\max }-\bar{v}_{\min }\) be the difference in maximum and minimum frequencies in \(\mathrm{cm}^{-1}\). The ratio \(\Delta \bar{v}\) \(\underset{\text { Lyman }} / \Delta \bar{v}_{\text {Balmer }}\) is : (a) \(4: 1\) (b) \(9: 4\) (c) \(5: 4\) (d) \(27: 5\)

The de Broglie wavelength of a car of mass \(1000 \mathrm{~kg}\) and velocity \(36 \mathrm{~km} / \mathrm{hr}\) is : [Main Online April 23, 2013] (a) \(6.626 \times 10^{-34} \mathrm{~m}\) (b) \(6.626 \times 10^{-38} \mathrm{~m}\) (c) \(6.626 \times 10^{-31} \mathrm{~m}\) (d) \(6.626 \times 10^{-30} \mathrm{~m}\)

The isoelectronic set of ions is (a) \(\mathrm{N}^{3-}, \mathrm{O}^{2-}, \mathrm{F}^{-}\)and \(\mathrm{Na}^{+}\) (b) \(\mathrm{N}^{3-}, \mathrm{Li}^{+}, \mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) (c) \(\mathrm{F}^{-}, \mathrm{Li}^{+}, \mathrm{Na}^{+}\)and \(\mathrm{Mg}^{2+}\) (d) \(\mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{O}^{2-}\) and \(\mathrm{F}^{-}\)

What is the work function of the metal if the light of wavelength \(4000 \AA\) generates photoelectrons of velocity \(6 \times 10^{5} \mathrm{~ms}^{-1}\) from it ? (Mass of electron= \(9 \times 10^{-31} \mathrm{~kg}\) Velocity of light \(=3 \times 10^{\circ} \mathrm{ms}^{-1}\) Planck's constant \(=6.626 \times 10^{-34} \mathrm{~J}_{\mathrm{S}}\) Charge of electron \(=1.6 \times 10^{-19} \mathrm{JeV}^{-1}\) ) (a) \(0.9 \mathrm{eV}\) (b) \(3.1 \mathrm{eV}\) (c) \(2.1 \mathrm{eV}\) (d) \(4.0 \mathrm{eV}\)

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 [2001S] (a) \(10^{-10} \mathrm{~m}\) (b) \(10^{-20} \mathrm{~m}\) (c) \(10^{-30} \mathrm{~m}\) (d) \(10^{-40} \mathrm{~m}\)

The quantum number of four electrons are given below: I. \(n=4, l=2, m_{l}=-2, m_{s}=-1 / 2\) II. \(n=3, l=2, m_{l}=1, m_{s}=+1 / 2\) III. \(n=4, l=1, m_{l}=0, m_{s}=+1 / 2\) IV. \(n=3, l=1, m_{l}=1, m_{\mathrm{s}}=-1 / 2\) The correct order of their increasing energies will be : (a) IV \(<\mathrm{III}<\mathrm{II}<\mathrm{I}\) (b) \(\mathrm{I}<\mathrm{II}<\mathrm{III}<\mathrm{IV}\) (c) \(\mathrm{IV}<\mathrm{II}<\mathrm{III}<\mathrm{I}\) (d) \(\mathrm{I}<\mathrm{III}<\mathrm{II}<\mathrm{IV}\)

Heat treatment of muscular pain involves radiation of wavelength of about 900 \(\mathrm{nm}\). Which spectral line of \(\mathrm{H}\)-atom is suitable for this purpose? [Main Jan. 11, 2019 (I)] \(\left[\mathrm{R}_{\mathrm{H}}=1 \times 10^{5} \mathrm{~cm}^{-1} . \mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right]\) (a) Paschen, \(\infty \rightarrow 3\) (b) Paschen, \(5 \rightarrow 3\) (c) Balmer, \(\infty \rightarrow 2\) (d) Lyman, \(\infty \rightarrow 1\)

Which of the following relates to photons both as wave motion and as a stream of particles? [1992-1 Mark] (a) Inference (b) \(E=m c^{2}\) (c) Diffraction (d) \(E=h v\)

The total number of orbitals associated with the principal quantum number 5 is : [Main Online April 9, 2016] (a) 20 (b) 25 (c) 10 (d) 5

The ground state energy of hydrogen atom is \(-13.6 \mathrm{eV}\). The energy of second excited state of \(\mathrm{He}^{+}\)ion in \(\mathrm{eV}\) is: (a) \(-54.4\) (b) \(-3.4\) (c) \(-6.04\) (d) \(-27.2\)

Which of the following statements is false? (a) Splitting of spectral lines in electrical field is called Stark effect (b) Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases (c) Photon has momentum as well as wavelength (d) Rydberg constant has unit of energy

The work function of sodium metal is \(4.41 \times 10^{-19} \mathrm{~J}\). If photons of wavelength \(300 \mathrm{~nm}\) are incident on the metal, the kinetic energy of the ejected electrons will be \(\left(h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s} ; c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\) \(\times 10^{-21} \mathrm{~J}\)

If the principal quantum number \(n=6\), the correct sequence of filling of electrons will be :[Main Online April 10,2015\(]\) (a) \(n s \rightarrow(n-2) f \rightarrow n p \rightarrow(n-1) d\) (b) \(n s \rightarrow(n-2) f \rightarrow(n-1) d \rightarrow n p\) (c) \(n s \rightarrow n p \rightarrow(n-1) d \rightarrow(n-2) f\) (d) \(n s \rightarrow(n-1) d \rightarrow(n-2) f \rightarrow n p\)

Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying \(0.5 \mathrm{~V}\) when the radiation of \(250 \mathrm{~nm}\) is used. The work function of the metal is : (a) \(4 \mathrm{eV}\) (b) \(5.5 \mathrm{eV}\) (c) \(4.5 \mathrm{eV}\) (d) \(5 \mathrm{eV}\)

Wave functions of electrons in atoms and molecules are called

The correct set of four quantum numbers for the valence electrons of rubidium atom \((Z=37)\) is: [Main 2014] (a) \(5,0,0,+\frac{1}{2}\) (b) \(5,1,0,+\frac{1}{2}\) (c) \(5,1,1,+\frac{1}{2}\) (d) \(5,0,1,+\frac{1}{2}\)

The radius of the second Bohr orbit for hydrogen atom is : (Plank's const. \(h=6.6262 \times 10^{-34} \mathrm{Js}\); mass of electron \(=9.1091 \times 10^{-31} \mathrm{~kg}\); charge of electron \(\mathrm{e}=1.60210 \times 10^{-19} \mathrm{C}\); permittivity of vaccum \(\left.\epsilon_{0}=8.854185 \times 10^{-12} \mathrm{~kg}^{-1} \mathrm{~m}^{-3} \mathrm{~A}^{2}\right)\) (a) \(1.65 \AA\) (b) \(4.76 \mathrm{~A}\) (c) \(0.529 \AA\) (d) \(2.12 \AA\)

The uncertainty principle and the concept of wave nature of matter were proposed by \(\ldots \ldots \ldots \ldots . .\) and \(\ldots \ldots \ldots \ldots \ldots\) respectively. (Heisenberg, Schrodinger, Maxwell, de Broglie)

In an atom how many orbital(s) will have the quantum numbers; \(n=3, l=2\) and \(m_{l}=+2 ?\) [Main Online April 9, 2013] (a) 5 (b) 3 (c) 1 (d) 7

If the shortest wavelength in Lyman series of hydrogen atom is \(\mathrm{A}\), then the longest wavelength in Paschen series of \(\mathrm{He}^{+}\)is : (a) \(\frac{5 \mathrm{~A}}{9}\) (b) \(\frac{9 \mathrm{~A}}{5}\) (c) \(\frac{36 \mathrm{~A}}{5}\) (d) \(\frac{36 \mathrm{~A}}{7}\)

Find the velocity \(\left(\mathrm{ms}^{-1}\right)\) of electron in first Bohr's orbit of radius \(a_{0}\). Also find the de Broglie's wavelength (in \(\mathrm{m}\) ). Find the orbital angular momentum of \(2 p\) orbital of hydrogen atom in units of \(h / 2 \pi\).

The number of radial nodes of \(3 s\) and \(2 p\) orbitals are respectively (a) 2,0 (b) 0,2 (c) 1,2 (d) 2,1

A stream of electrons from a heated filaments was passed two charged plates kept at a potential difference \(\mathrm{V}\) esu. If 'e' and \(m\) are charge and mass of an electron, respectively, then the value of \(h / \lambda\) (where \(\lambda\) is wavelength associated with electron wave) is given by: (a) \(\sqrt{m \mathrm{eV}}\) (b) \(\sqrt{2 m \mathrm{eV}}\) (c) \(m \mathrm{eV}\) (d) \(2 \mathrm{meV}\)

A ball of mass \(100 \mathrm{~g}\) is moving with \(100 \mathrm{~ms}^{-1}\). Find its wavelength.

If the nitrogen atom has electronic configuration \(1 s^{7}\), it would have energy lower than that of the normal ground state configuration \(1 s^{2} 2 s^{2} 2 p^{3}\), because the electrons would be closer to the nucleus. Yet \(1 s^{7}\) is not observed because it violates. [2002S] (a) Heisenberg uncertainty principle (b) Hund's rule (c) Pauli exclusion principle (d) Bohr postulate of stationary orbits

Which of the following is the energy of a possible excited state of hydrogen ? (a) \(-3.4 \mathrm{eV}\) (b) \(+6.8 \mathrm{eV}\) (c) \(+13.6 \mathrm{eV}\) (d) \(-6.8 \mathrm{eV}\)

The quantum numbers \(+1 / 2\) and \(-1 / 2\) for the electron spin represent [2001S] (a) rotation of the electron in clockwise and anticlockwise direction respectively (b) rotation of the electron in anticlockwise and clockwise direction respectively (c) magnetic moment of the electron pointing up and down respectively (d) two quantum mechanical spin states which have no classical analogue

If \(m\) and \(e\) are the mass and charge of the revolving electron in the orbit of radius \(r\) for hydrogen atom, the total energy of the revolving electron will be: (a) \(\frac{1}{2} \frac{e^{2}}{r}\) (b) \(-\frac{e^{2}}{r}\) (c) \(\frac{m e^{2}}{r}\) (d) \(-\frac{1}{2} \frac{e^{2}}{r}\)

The electronic configuration of an element is \(1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{3}, 4 s^{1} .\) This represents its [2000S] (a) excited state (b) ground state (c) cationic form (d) anionic form

If \(\lambda_{0}\) and \(\lambda\) be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is: (a) \(\sqrt{\frac{2 h}{m}\left(\lambda_{0}-\lambda\right)}\) (b) \(\sqrt{\frac{2 h c}{m}\left(\lambda_{0}-\lambda\right)}\) (c) \(\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_{0}-\lambda}{\lambda \lambda_{0}}\right)}\) (d) \(\sqrt{\frac{2 h}{m}\left(\frac{1}{\lambda_{0}}-\frac{1}{\lambda}\right)}\)

The number of nodal planes in a \(p_{x}\) orbital is (a) one (b) two (c) three

Energy of an electron is given by \(\mathrm{E}=-2.178 \times 10^{-18} \mathrm{~J}\left(\frac{Z^{2}}{n^{2}}\right)\). Wavelength of light required to excite an electron in an hydrogen atom from level \(n=1\) to \(n=2\) will be: \(\left(h=6.62 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right.\) and \(\left.\mathrm{c}=3.0 \times 10^{\mathrm{s}} \mathrm{ms}^{-1}\right)\) (a) \(1.214 \times 10^{-7} \mathrm{~m}\) (b) \(2.816 \times 10^{-7} \mathrm{~m}\) (c) \(6.500 \times 10^{-7} \mathrm{~m}\) (d) \(8.500 \times 10^{-7} \mathrm{~m}\)

The electrons, identified by quantum numbers \(n\) and \(l\), (i) \(n=4, l=1\), (ii) \(n=4, l\) \(=0\), (iii) \(n=3, l=2\), and (iv) \(n=3, l=1\) can be placed in order of increasing energy, from the lowest to highest, as [1999-2 Marks] (a) (iv) \(<(\) ii \()<(\) iii \()<\) (i) (b) (ii) \(<\) (iv) \(<(\mathrm{i})<(\mathrm{iii})\) (c) (i) \(<(\) iii \()<(\) ii \()<\) (iv) (d) (iii) \(<(\mathrm{i})<(\mathrm{iv})<(\mathrm{ii})\)

The wave number of the first emission line in the Balmer series of \(\mathrm{H}\)-Spectrum is: \((\mathrm{R}=\) Rydberg constant \()\) : (a) \(\frac{5}{36} R\) (b) \(\frac{9}{400} R\) (c) \(\frac{7}{6} R\) (d) \(\frac{3}{4} R\)