JEE Advanced 2017 Paper 1 Chemistry Q14

Chemistry · The Hydrogen Atom & Atomic Structure

Problem

Answer Q.13, Q.14 and Q.15 by appropriately matching the information given in the three columns of the following table. The wave function,

\psi_{n,l,m_l}

, is a mathematical function whose value depends upon spherical polar coordinates

(r, \theta, \phi)

of the electron and characterized by the quantum numbers

n

l

and

m_l

. Here

r

is distance from nucleus,

\theta

is colatitude and

\phi

is azimuth. In the mathematical functions given in the Table,

Z

is atomic number and

a_o

is Bohr radius. Column 1 — (I) 1s orbital; (II) 2s orbital; (III) 2p_z orbital; (IV) 3d_{z^2} orbital Column 2 — (i)

\psi \propto (Z/a_o)^{3/2}e^{-Zr/a_o}

; (ii) One radial node; (iii)

\psi \propto (Z/a_o)^{5/2}r e^{-Zr/(2a_o)}\cos\theta

; (iv) xy-plane is a nodal plane Column 3 — (P) Plotted radial wave function with exactly one radial node; (Q) Probability density at nucleus

\propto 1/a_o^3

; (R) Probability density is maximum at nucleus; (S)

E_{2\to4}/E_{2\to6}=27/32

For hydrogen atom, the only CORRECT combination is