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 hydrogen atom, the only CORRECT combination is

Accepted Answer

(A) (I) (i) (S)

Answer

(B) (II) (i) (Q)

Answer

(C) (I) (i) (P)

Answer

(D) (I) (iv) (R)

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