Question

| Column 1 | Column 2 | Column 3 |
| --- | --- | --- |
| (I) 1s orbital | (i) $\psi_{n,l,m_l} \propto \left(\frac{Z}{a_o}\right)^{\frac{3}{2}} e^{-\left(\frac{Zr}{a_o}\right)}$ | (P) |
| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus $\propto \frac{1}{a_0^3}$ |
| (III) $2p_z$ orbital | (iii) $\psi_{n,l,m_l} \propto \left(\frac{Z}{a_o}\right)^{\frac{5}{2}} r e^{-\left(\frac{Zr}{2a_o}\right)} \cos\theta$ | (R) Probability density is maximum at nucleus |
| (IV) $3d_{z^2}$ orbital | (iv) $xy$-plane is a nodal plane | (S) Energy needed to excite electron from $n=2$ state to $n=4$ state is $\frac{27}{32}$ times the energy needed to excite electron from $n=2$ state to $n=6$ state |

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.

For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is

Accepted Answer

(C) (II) (ii) (P)

Answer

(A) (I) (ii) (S)

Answer

(B) (IV) (iv) (R)

Answer

(D) (III) (iii) (P)

JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Atomic Structure

Solution

More JEE Advanced questions on Atomic Structure

Column 1	Column 2	Column 3
(I) 1s orbital	(i) $ψ_{n, l, m_{l}} \propto (\frac{Z}{a _{o}})^{\frac{3}{2}} e^{- (\frac{Z r}{a _{o}})}$	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a _{0}^{3}}$
(III) $2 p_{z}$ orbital	(iii) $ψ_{n, l, m_{l}} \propto (\frac{Z}{a _{o}})^{\frac{5}{2}} r e^{- (\frac{Z r}{2 a _{o}})} cos θ$	(R) Probability density is maximum at nucleus
(IV) $3 d_{z^{2}}$ orbital	(iv) $x y$ -plane is a nodal plane	(S) Energy needed to excite electron from $n = 2$ state to $n = 4$ state is $\frac{27}{32}$ times the energy needed to excite electron from $n = 2$ state to $n = 6$ state