JEE Advanced 2017 · Paper 1 · Chemistry Q14

← JEE Advanced 2017 · Paper 1

ChemistrySingle correct+3 / -1Question 32 of 54

Passage

Answer Q.31, Q.32 and Q.33 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	Column 2	Column 3
(I) 1s orbital	(i) $\psi_{n,l,m_l} \propto \left(\frac{Z}{a_o}\right)^{3/2} e^{-\left(\frac{Zr}{a_o}\right)}$	(P) [plot of $\psi_{n,l,m_l}(r)$ against $r/a_0$ ]
(II) 2s orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a_o^3}$
(III) $2p_z$ orbital	(iii) $\psi_{n,l,m_l} \propto \left(\frac{Z}{a_o}\right)^{5/2} r e^{-\left(\frac{Zr}{2a_o}\right)} \cos\theta$	(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 three-column table for Q.31-33. Column 3 entry (P) is a plot of ψ(r) against r/a₀: the curve starts high at r = 0, falls steeply, crosses zero once (one radial node), dips to a shallow negative minimum and rises back towards zero.

For hydrogen atom, the only CORRECT combination is

(I) (i) (S)

(II) (i) (Q)

(I) (i) (P)

(I) (iv) (R)

Answer and worked solution

Official answer: A

1s orbital. Its wavefunction is (i), $\psi\propto(Z/a_0)^{3/2}e^{-Zr/a_0}$ .

Energy ratio (S).
$\frac{E_{2\to4}}{E_{2\to6}}=\frac{\frac14-\frac1{16}}{\frac14-\frac1{36}}=\frac{3/16}{8/36}=\frac{27}{32}.$
This holds for hydrogen.

So (I)(i)(S) is correct. In the other options: (II) with (i) mismatches the function; (P) is a 2s plot; (iv) is wrong for 1s.

(A)

Topics:Orbitals and their shapes Bohr model

← Previous question Next question →

JEE Advanced 2017 · Paper 1, Chemistry question 14