Which of the following statements concerning
Question: Which of the following statements concerning the quantum numbers are correct? (i) The angular quantum number determines the three-dimensional shape of the orbital. (ii) The principal quantum number determines the orientation and energy of the orbital. (iii) The magnetic quantum number determines the size of the orbital. (iv) Spin quantum number of an electron determines the orientation of the spin of the electron relative to the chosen axis. Solution: Option (i) and (iv) are the answer...
Read More →In which of the following pairs,
Question: In which of the following pairs, the ions are iso-electronic? (i) Na+, Mg2+ (ii) Al3+, O (iii) Na+, O2- (iv) N3-, Cl Solution: Option (i)Na+, Mg2+ and (iii)Na+, O2-are the answers....
Read More →Find the equation
Question: Find the equation of the tangent and the normal to the following curves at the indicated points: $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1$ at $(\mathrm{a} \sec \theta, \mathrm{b} \tan \theta)$ Solution: finding the slope of the tangent by differentiating the curve $\frac{x}{a^{2}}-\frac{y}{b^{2}} \frac{d y}{d x}=0$ $\frac{d y}{d x}=\frac{x b^{2}}{y a^{2}}$ $\mathrm{m}(\operatorname{tangent})$ at $(\mathrm{a} \sec \theta, \mathrm{b} \tan \theta)=\f...
Read More →Which of the following sets
Question: Which of the following sets of quantum numbers is correct? n l ml (i) 1 1 +2 (ii) 2 1 +1 (iii) 3 2 2 (iv) 3 4 2 Solution: Option (ii)2 1 +1 and (iii) 3 2 2are the answers...
Read More →Find the equation
Question: Find the equation of the tangent and the normal to the following curves at the indicated points: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ at $(a \cos \theta, b \sin \theta)$ Solution: finding the slope of the tangent by differentiating the curve $\frac{x}{a^{2}}+\frac{y}{b^{2}} \frac{d y}{d x}=0$ $\frac{d y}{d x}=-\frac{x a^{2}}{y b^{2}}$ $\mathrm{m}(\operatorname{tangent}) \mathrm{at}(\mathrm{a} \cos \theta, \mathrm{b} \sin \theta)=-\frac{\cot \theta \mathrm{a}^{2}}{\mathrm{~b}^{2}...
Read More →Out of the following pairs of electrons,
Question: Out of the following pairs of electrons, identify the pairs of electrons present in degenerate orbitals : (i) (a) n = 3, l = 2, ml = 2, ms= 1/2 (b) n = 3, l = 2, ml = 1, ms= 1/2 (ii) (a) n = 3, l = 1, ml = 1, ms = +1/2 (b) n = 3, l = 2, ml = 1, ms = +1/2 (iii) (a) n = 4, l = 1, ml = 1, ms = +1/2 (b) n = 3, l = 2, ml = 1, ms = +1/2 (iv) (a) n = 3, l = 2, ml = +2, ms = 1/2 (b) n = 3, l = 2, ml = +2, ms = +1/2 Solution: Option (i) and (iv) are the answers....
Read More →Identify the pairs which are not
Question: Identify the pairs which are not of isotopes? (i)6X12,6Y13 (ii)17X35,6Y37 (iii)6X14,7Y14 (iv)4X8,5Y8 Solution: Option (iii)6X14,7Y14 and (iv)4X8,5Y8are the answers....
Read More →Find the equation
Question: Find the equation of the tangent and the normal to the following curves at the indicated points: $y=x^{2}+4 x+1$ at $x=3$ Solution: finding slope of the tangent by differentiating the curve $\frac{d y}{d x}=2 x+4$ $\mathrm{m}$ (tangent) at $(3,0)=10$ normal is perpendicular to tangent so, $m_{1} m_{2}=-1$ $\mathrm{m}$ (normal) at $(3,0)=-\frac{1}{10}$ equation of tangent is given by $\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}$ (tangent) $\left(\mathrm{x}-\mathrm{x}_{1}\right)$ $y$ at $x=3$ $...
Read More →If travelling at the same speeds,
Question: If travelling at the same speeds, which of the following matter waves have the shortest wavelength? (i) Electron (ii) An alpha particle (He2+) (iii) Neutron (iv) Proton Solution: Option (ii)An alpha particle (He2+)is the answer....
Read More →Find the general solution of each of the following equations:
Question: Find the general solution of each of the following equations: cot x + tan x = 2 cosec x Solution: To Find: General solution. Given: $\cot x+\tan x=2 \operatorname{cosec} x \Rightarrow \cos ^{2} x+\sin ^{2} x=2 \sin x \cos x \operatorname{cosec} x \Rightarrow 1=\sin 2 x$ cosec $x$ $\Rightarrow \operatorname{cosec} 2 x=\operatorname{cosec} x \Rightarrow \sin x=\sin 2 x \Rightarrow \sin x=2 \sin x \cos x \Rightarrow \sin x=0$ or $\cos$ $x=\frac{1}{2}=\cos (1)$ Formula used: $\sin \theta=0...
Read More →For the electrons of an oxygen atom,
Question: For the electrons of an oxygen atom, which of the following statements is correct? (i) Zeff for an electron in a 2s orbital is the same as Zeff for an electron in a 2p orbital. (ii) An electron in the 2s orbital has the same energy as an electron in the 2p orbital. (iii) Zeff for an electron in 1s orbital is the same as Zeff for an electron in a 2s orbital. (iv) The two electrons present in the 2s orbital have spin quantum numbers ms but of opposite sign. Solution: Option (iv)The two e...
Read More →The pair of ions having same electronic
Question: The pair of ions having same electronic configuration is __________. (i) Cr3+, Fe3+ (ii) Fe3+, Mn2+ (iii) Fe3+, Co3+ (iv) Sc3+, Cr3+ Solution: Option (ii)Fe3+, Mn2+is the answer....
Read More →Chlorine exists in two isotopic forms,
Question: Chlorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately (i) 1:2 (ii) 1:1 (iii) 1:3 (iv) 3:1 Solution: Option (iii)1:3 is the answer....
Read More →Find the general solution of each of the following equations:
Question: Find the general solution of each of the following equations: $\sin x \tan x-1=\tan x-\sin x$ Solution: To Find: General solution. Given: $\sin x \tan x-1=\tan x-\sin x \Rightarrow \sin x(\tan x+1)=\tan x+1$ So $\sin x=1=\sin \left(\frac{\pi}{2}\right)$ or $\tan x=-1=\tan \left(\frac{3 \pi}{4}\right)$ Formula used: $\sin \theta=\sin \alpha \Rightarrow \theta=\mathrm{n} \pi+(-1)^{\mathrm{n}} \alpha, \mathrm{n} \in \mid$ and $\tan \theta=\tan \alpha \Rightarrow \theta=\mathrm{k}$ $\pi+\a...
Read More →Orbital angular momentum depends
Question: Orbital angular momentum depends on __________. (i) l (ii) n and l (iii) n and m (iv) m and s Solution: Option (i)l is the answer....
Read More →Find the general solution of each of the following equations:
Question: Find the general solution of each of the following equations: $2 \tan x-\cot x+1=0$ Solution: To Find: General solution. Given: $2 \tan x-\cot x+1=0 \Rightarrow 2 \tan ^{2} x-1+\tan x=0 \Rightarrow 2 \tan ^{2} x-1+2 \tan x-\tan x=$ $0 \Rightarrow 2 \tan x(\tan x+1)-(1+\tan x)=0$ $\Rightarrow(2 \tan x-1)(1+\tan x)=0 \Rightarrow \tan x=\frac{1}{2}=\tan ^{-1} \frac{1}{2}$ or $\tan x=-1=\tan \frac{3 \pi}{4}$ Formula used: $\tan \theta=\tan \alpha \Rightarrow \theta=\mathrm{n} \pi+\alpha, \...
Read More →A total number of orbitals associated
Question: A total number of orbitals associated with the third shell will be __________. (i) 2 (ii) 4 (iii) 9 (iv) 3 Solution: Option (iii)9 is the answer....
Read More →Which of the following is responsible
Question: Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons? (i) Paulis exclusion principle. (ii) Heisenbergs uncertainty principle. (iii) Hunds rule of maximum multiplicity. (iv) Aufbau principle. Solution: Option (ii)Heisenbergs uncertainty principleis the answer....
Read More →Number of angular nodes
Question: Number of angular nodes for 4d orbital is __________. (i) 4 (ii) 3 (iii) 2 (iv) 1 Solution: Option (iii) 2 is the answer....
Read More →Find the general solution of each of the following equations:
Question: Find the general solution of each of the following equations: $\sqrt{3} \cos x+\sin x=1$ Solution: To Find: General solution. Given: $\sqrt{3} \cos x+\sin x=1 \Rightarrow \cos \left(x-\frac{\pi}{6}\right)=\frac{1}{2}=\cos \left(\frac{\pi}{3}\right)$ or $\cos \left(\frac{5 \pi}{3}\right)$ [Divide $\sqrt{2}$ on both sides and $\cos (x-y)=\cos x \cos y-\sin x \sin y$ ] Formula used: $\cos \theta=\cos \alpha \Rightarrow \theta=2 n \pi \pm \alpha$ By using above formula, we have $\Rightarro...
Read More →The number of radial nodes for
Question: The number of radial nodes for 3p orbital is __________. (i) 3 (ii) 4 (iii) 2 (iv) 1 Solution: Option (iv) 1 is the answer....
Read More →Two atoms are said to be isobars if.
Question: Two atoms are said to be isobars if. (i) they have the same atomic number but a different mass number. (ii) they have the same number of electrons but a different number of neutrons. (iii) they have the same number of neutrons but a different number of electrons. (iv) the sum of the number of protons and neutrons is the same but the number of protons is different. Solution: Option (iv)the sum of the number of protons and neutrons is the same but the number of protons is different is th...
Read More →Which of the following properties
Question: Which of the following properties of an atom could be explained correctly by Thomson Model of an atom? (i) Overall neutrality of atom. (ii) Spectra of a hydrogen atom. (iii) Position of electrons, protons and neutrons in an atom. (iv) Stability of atom. Solution: Option (i)Overall neutrality of atom is the answer....
Read More →Find the general solution of each of the following equations:
Question: Find the general solution of each of the following equations: $\cos x-\sin x=-1$ Solution: To Find: General solution. Given: $\cos x-\sin x=1 \Longrightarrow \cos \left(x+\frac{\pi}{4}\right)=\frac{-1}{\sqrt{2}}=\cos \frac{3 \pi}{4}$ [divide $\sqrt{2}$ on both sides and $\cos (x-y)=\cos x \cos y-\sin x \sin y$ ] So $\sin x=0$ or $\cos x=0$ Formula used: $\cos \theta=\cos \alpha \Rightarrow \theta=2 k \pi \pm \alpha, k \in I$ $\Rightarrow x+\frac{\pi}{4}=2 k \pi \pm \frac{3 \pi}{4} \Rig...
Read More →Which of the following statements
Question: Which of the following statements about the electron is incorrect? (i) It is a negatively charged particle. (ii) The mass of an electron is equal to the mass of a neutron. (iii) It is a basic constituent of all atoms. (iv) It is a constituent of cathode rays. Solution: Option (ii)The mass of an electron is equal to the mass of a neutronis the answer....
Read More →