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JEE Advanced 2017 Paper 1

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The wave function,ψn,l,ml\psi_{n,l,m_l}is a mathematical function whose value depends upon spherical polar coordinates (r,θ,ϕr, \theta, \phi) of the electron and characterized by the quantum numbersn,ln, landmlm_l. Hererris distance from nucleus,θ\thetais colatitude andϕ\phiis azimuth. In the mathematical functions given in the Table,ZZis atomic number andaoa_ois Bohr radius.
Column 1 Column 2 Column 3
(I) 1s orbital (i) ψn,l,ml(Za0)3/2ezxa0\psi_{n,l,m_l} \propto \left(\frac{Z}{a_0}\right)^{3/2} e^{-\frac{zx}{a_0}}
(II) 2s orbital (ii) One radial node (Q) Probability density at nucleus 1a03\propto \frac{1}{a_0^3}
(III) 2pz2p_z orbital (iii) ψn,l,ml(Za0)3/2rezxa0cosθ\psi_{n,l,m_l} \propto \left(\frac{Z}{a_0}\right)^{3/2} r e^{-\frac{zx}{a_0}} \cos \theta (R) Probability density is maximum at nucleus
(IV) 3dz23d^{2}_{z} orbital (iv) xy-plane is a nodal plane (S) Energy needed to excite electron from n=2n = 2 state to n=4n = 4 state is 2732\frac{27}{32} times the energy needed to excite electron from n=2n = 2 state to n=6n = 6 state
Section: Chemistry
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